In a recent article, we have corrected the traditional derivation of the Schwarzschild metric, thus obtaining the formulation of the correct Schwarzschild metric, which is different from the traditional Schwarzschild ...In a recent article, we have corrected the traditional derivation of the Schwarzschild metric, thus obtaining the formulation of the correct Schwarzschild metric, which is different from the traditional Schwarzschild metric. Then, in another article by starting from this correct Schwarzschild metric, we have corrected also the Reissner-Nordstrøm, Kerr and Kerr-Newman metrics. On the other hand, in a third article, always by starting from this correct Schwarzschild metric, we have obtained the formulas of the correct gravitational potential and of the correct gravitational force in the case described by this metric. Now, in this article, by starting from these correct Reissner-Nordstrøm, Kerr and Kerr-Newman metrics and proceeding in a manner analogous to this third article, we obtain the formulas of the correct gravitational potential and of the correct gravitational force in the cases described by these metrics. Moreover, we analyze these correct results and their consequences. Finally, we propose some possible crucial experiments between the commonly accepted theory and the same theory corrected according to this article.展开更多
The paper is devoted to the study of the gravitational collapse within the framework of the spherically symmetric problem in the Newton theory and general relativity on the basis of the pressure-free model of the cont...The paper is devoted to the study of the gravitational collapse within the framework of the spherically symmetric problem in the Newton theory and general relativity on the basis of the pressure-free model of the continuum. In application to the Newton gravitation theory, the analysis consists of three stages. First, we assume that the gravitational force is determined by the initial sphere radius and constant density and does not change in the process of the sphere collapse. The obtained analytical solution allows us to find the collapse time in the first approximation. Second, we construct the step-by-step process in which the gravitational force at a given time moment depends on the current sphere radius and density. The obtained numerical solution specifies the collapse time depending on the number of steps. Third, we find the exact value of the collapse time which is the limit of the step-by-step solutions and study the collapse and the expansion processes in the Newton theory. In application to general relativity, we use the space model corresponding to the special four-dimensional space which is Euclidean with respect to space coordinates and Riemannian with respect to the time coordinate only. The obtained solution specifies two possible scenarios. First, sphere contraction results in the infinitely high density with the finite collapse time, which does not coincide with the conventional result corresponding to the Schwarzschild geometry. Second, sphere expansion with the velocity which increases with a distance from the sphere center and decreases with time.展开更多
The discovery by the author of real magnetic charges and true anti-electrons in the atomic structures allowed him to establish that the gravitational field (GF) in reality is the vortex electromagnetic field. Dependin...The discovery by the author of real magnetic charges and true anti-electrons in the atomic structures allowed him to establish that the gravitational field (GF) in reality is the vortex electromagnetic field. Depending on the vector conditions the gravitational fields can be either paragravitational (PGF) or ferrogravitational (FGF). Masses (atoms, nucleons, etc.) emitting PGF manifest so-called attraction to each other. In fact, this process is the pressing of atoms or nucleons to each other by the forces of gravitational “Dark energy”. Namely the gravitational “Dark energy” which is formed between the masses emitting PGF and compressing of nucleons in atomic nuclei is the main force factor determining the formation of nuclear forces. Masses that emit FGF are repelled from PGF sources, for example, from the Earth. The last gravitational manifestation, discovered by the author, this is of the effect of the gravitational levitation. The atomic shell and atomic nucleus are autonomous sources of gravitational field in atomic compositions. The gravitational fields emitted these sources, by its physical parameters, are different gravitational fields, what associated with differences in the magnitudes charges of magnetic and electric particles in their compositions. The noted differences in the parameters of the GF are of reason that in atoms the process of extrusion of foreign gravitational field from the region of given gravitational source is realized. This effect should be called the effect of intra-atomic gravitational shielding (IAGS). Within the framework of this effect the shell of the atom is a kind of gravitational “insulator” that prevents the PGF of the nucleons from leaving beyond of the atom. As result of the IAGS effect, the concentration PGF of nucleons is realized only in the region of the nucleus, which leads to an increase in nuclear forces. However, the resistance of the marked “insulator” is finite and if the critical voltage PGF on the nucleus is exceeded, the complete shielding of the nucleon fields by the atomic shell is broken. As result of the leakage of a part of the PGF of nucleons beyond the atom, the density of this field in the region of the nucleus decreases significantly, which leads to a weakening of the nuclear forces and often leads to radioactivity. The effect of gravitational shielding is directly related to such a well-known concept as the mass defect of the nucleus. It is the exclusion of the gravitational field formed by the nucleons in the composition of the atomic nucleus as a result of the full IAGS effect that creates the illusion of atomic mass defect.展开更多
In the article ＂The Gravitational Force Quantum and its Value＂ [1 ], the author defined a gravitational force of the atomic unit （＂the Gravitational Force Quantum＂） as a gravitational force which exerts one atom...In the article ＂The Gravitational Force Quantum and its Value＂ [1 ], the author defined a gravitational force of the atomic unit （＂the Gravitational Force Quantum＂） as a gravitational force which exerts one atomic unit of the Earth＇s mass on l kilogram of a mass on the Earth＇s surface, and he calculated its value as： GFQEarth = 1.4958 × 10.54 N. In the present contribution, he extended the Gravitational Force Quantum concept to further Objects of the Solar Planetary System and for the Pluto. He calculated values of the GFQo on the analogous basis, i.e. of the mass and the standard acceleration of the gravity of individual objects and of the atomic unit of the mass. He received GFQo values for the Mercury 102.1427 × 1055N, the Venus 16,60012 × 10-55N, the Earth 14.97839 × l0-55 N, the Mars 52.91869 × 10-55N, the Jupiter 0.124391×1055 N, the Saturn 0.17929 ×1055N, the Uranus 0.945178 ×1055N, the Neptune 1.002845 × 10-55N, for the Pluto 458.9124 × 10-55N, and for the Sun 0.001257 × 10-55N, respectively. He multiplied the GFQo values by second power of the radii of the individual objects （O）, receiving values denoted as the ＂Elementary Gravitational Charge＂ （Go）. The Elementary Gravitational Charge represents a gravitational force of one atomic unit of mass in the （radius） distance of 1 meter. They were found of the same value： GMe= Gv = GE= GMa= Gj= Gs = Gp= GSun= 6.079675463 × 10-41N. The values were the same as the calculated one on the basis of the ＂classical＂ Newton＇s formula： FG = И × M × m / R2, for the gravitational force between the atomic unit mass and a mass of 1 kg at a distance of 1 meter, which value was calculated as G = 6.079675463 ×1041 N. The quantity of the Elementary Gravitational Charge can be supposed to be analogous to the Elementary （Electric） Charge （e =1.6021766208（98） × 10-19 C） quantity.展开更多
The study by the author of magnetic scattering neutrons in the structures of ferrimagnets, as well as his experiments with the separation of magnetic charges in dipole pairs ±g in magnetic field, showed that fund...The study by the author of magnetic scattering neutrons in the structures of ferrimagnets, as well as his experiments with the separation of magnetic charges in dipole pairs ±g in magnetic field, showed that fundamental magnetic particles (magnetic charges) are real structural components of atoms and substance. It is the magnetic poles, and not the moving electric charges are the direct sources of all magnetic fields and magnetic manifestations in Nature. Basic reasons of ignoring the magnetic fundamental particles by world physical theory, for almost 150 years, are the ultra-harsh confinement of these particles in substance which radically is different from the confinement electrons, as well as the vicious concept of the electric magnetism Maxwell. Rotating magnetic dipoles in conductors which are untwisted by electric current, are direct sources of the vortex magnetic field rot<em><strong>H</strong></em>. One should also expect the formation of a vortex electric field rot<em><strong>E </strong></em>forming by rotating electric dipoles which are untwisted by the current of magnetic charges. This article provides an experimental answer to the question: what field is formed around a conductor if joint direct currents of electric<em> <strong style="white-space:normal;"><em>J</em></strong></em><sub>e</sub> and magnetic<strong><em> J</em></strong><sub>g</sub> charges are passed through it? The author’s experiments have shown that in this case the vortex electromagnetic current is realized which manifests itself as the vortex electromagnetic (gravitational) field. It is possible to implement such a process, according to the results of the author’s research, exclusively in superconductors. The vector character of the gravitational field is in many respects similar to the vortex magnetic field which makes it possible to introduce such it states as paragravitation and ferrogravitation into representations. To create joint currents of electric and magnetic charges, the author used the inertial forces of these particles under conditions of acceleration and deceleration of the rotational motion of the closed lead superconductor. The result of this experiment was the gravitational, as it turned out later, the ferrogravitational field, which was detected by effect repulsion of trial cargos from the coil with a superconducting winding at the stage of its untwist. The latter process is defined by the author as an effect of the gravitational (ferrogravitational) levitation. The values of ferrogravitational (levitational) forces noted in this experiment were: 120 mg for a tungsten trial cargo and 50 and 25 mg for a lead cargo with an error of ±15 mg. The values of ferrogravitational (levitational) forces noted in this experiment are: 120 mg for from tungsten trial cargo and 50 and 25 mg for a cargo from lead, with an error of ±15 mg. The “anomaly” noted by the author in this study was in the absence of any absence of a gravitational effect on stage a braking of the coil. Probable cause of the noted “anomaly” is discussed in the Discussion of Results chapter.展开更多
As is generally known, Newton＇s notion of universal gravitation surpassed various theories of particular gravities in the early modem age, as represented mainly by Kepler and Hooke. In his seminal work Hooke and the ...As is generally known, Newton＇s notion of universal gravitation surpassed various theories of particular gravities in the early modem age, as represented mainly by Kepler and Hooke. In his seminal work Hooke and the Law of Universal Gravitation： A Reappraisal of a Reappraisal Richard S. Westfall argues that Hooke could not reach beyond the concept of spatially bounded particular gravities, as he deployed the method of analogy between the material principle of congruity and incongruity and the extension of gravitational spheres and their action at a distance. However, the doctrine of universal gravitation does not exclude the nature of particular gravities; it is predicated on the notion of an infinite expansion of individual-gravitational spheres and their uniform nature, namely the mutual and centripetal attraction. In my treatise 1 attempt to reinvestigate the nature and structure of gravitation, as established historically in the framework of Newtonian Classical Mechanics, by a method of structural intuition. It examines how the structural intuition, as represented in the celestial-mechanical intuitions of Hooke and Kepler, could unfold into an innovative process within the context of early modem mechanical philosophy, attaining thus a historical siglaificance and legitimacy as against the prevailing Newtonian method of geometric-mathematical axiomatization of mechanical principles. It also explores the actual demonstrative features of the tidal phenomenon with regard to its lunar- and solar-gravitational causation, which has been considered to date to be an important piece of empirical evidence for the theory of universal gravitation.展开更多
The study of the effect of the gravitational field on the photons, based on the hypothesis of the absolute reference system, demonstrates the origin of the gravitational force. By studying the propagation of a photon ...The study of the effect of the gravitational field on the photons, based on the hypothesis of the absolute reference system, demonstrates the origin of the gravitational force. By studying the propagation of a photon in the gravitational field the change in the estimation of time is determined, resulting from the use of a clock that is affected by the gravitational field. It is proved that in all known experiments, which were carried out in order to confirm the general theory of relativity, the results based on the hypothesis of an absolute reference system agree with the corresponding results of the general theory of relativity, except for the result of the deflection of light in the gravitational field of the sun, where the experimental results confirm the hypothesis of the absolute reference system.展开更多
Exoplanet imaging using the solar gravitational lens is an enticing prospect.The fundamental physical properties of the lens,including its angular resolution and light amplification,promise exceptional capabilities.Th...Exoplanet imaging using the solar gravitational lens is an enticing prospect.The fundamental physical properties of the lens,including its angular resolution and light amplification,promise exceptional capabilities.These expectations,however,are tempered by the realization of numerous challenges,including imperfections of the lens itself,noise sources,the properties of the imaging target and difficult technical issues.We discuss,in particular,a subject not previously addressed,the impact of temporally varying surface features,notably a variable cloud cover,obscuring the target exoplanet.This has a substantial detrimental effect on image recovery,leading to our cautious assessment of the practical feasibility of using the Sun’s gravitational field as an effective telescope.展开更多
The Newtonian gravitational constant G is one of the most important fundamental constants of nature, but still remains resistant to the standard model of physics and disconnected from quantum theory. During the past &...The Newtonian gravitational constant G is one of the most important fundamental constants of nature, but still remains resistant to the standard model of physics and disconnected from quantum theory. During the past >100 years, hundreds of G values have been measured to be ranging around 6.66 to 6.7559 × 10−11 m3·kg−1·s−2 using macroscopic masses. More recently, however, a G value ((6.04 ± 0.06) × 10−11 m3·kg−1·s−2) measured using millimetre-sized masses shows significant deviation (by ~9%) from the reference G value, which the authors explained is resulted from “the known systematic uncertainties”. However, based on the observation of historical G values and the protocol of the millimetre-sized masses based experiment, here we proposed a theory that this deviation is not from “systematic uncertainties” but actually G will rapidly decrease when masses sphere diameter is less than 0.02 metres. Moreover, this theory predicted the G value will be 5.96 × 10−11 m3·kg−1·s−2 between masses whose diameter are 2 millimetres (0.002 metres), which matches the measured G value very well.展开更多
We present a theoretical model for detecting axions from neutron stars in a QCD phase of quark matter. The axions would be produced from a quark-antiquark pair uu¯or dd¯, in loop(s) involving gluons. The chi...We present a theoretical model for detecting axions from neutron stars in a QCD phase of quark matter. The axions would be produced from a quark-antiquark pair uu¯or dd¯, in loop(s) involving gluons. The chiral anomaly of QCD and the spontaneously broken symmetry are invoked to explain the non-conservation of the axion current. From the coupling form factors, the axion emissivities ϵacan be derived, from which fluxes can be determined. We predict a photon flux, which may be detectable by Fermi LAT, and limits on the QCD mass ma. In this model, axions decay to gamma rays in a 2-photon vertex. We may determine the expected fluxes from the theoretical emissivity. The sensitivity curve from the Fermi Large Area Telescope (Fermi LAT) would allow axion mass constraints for neutron stars as low as ma≤10−14eV 95% C.L. Axions could thus be detectable in gamma rays for neutron stars as distant as 100 kpc. A signal from LIGO GWS 170817 could be placed from the NS-NS merger, which gives an upper limit of ma≤10−10eV.展开更多
Einstein aimed to find a unified theoretical model to explain various interactions in nature,and the relationship between gravitational and electric fields was particularly important.For the first time,this paper prov...Einstein aimed to find a unified theoretical model to explain various interactions in nature,and the relationship between gravitational and electric fields was particularly important.For the first time,this paper provides the internal relationship equations of the electric and magnetic fields.Further,the relationship between the magnetic and gravity fields is analyzed,and the relationship equations of the electric,magnetic,and gravity fields are established.On this basis,a general formula for calculating the radius of charged particles is derived.Simultaneously,we also discussed and made predictions on black holes,providing convenience for future research and experimental detection.展开更多
Research on the properties of neutron stars with dark energy is a particularly interesting yet unresolved problem in astrophysics.We analyze the influence of dark energy on the equation of state,the maximum mass,the s...Research on the properties of neutron stars with dark energy is a particularly interesting yet unresolved problem in astrophysics.We analyze the influence of dark energy on the equation of state,the maximum mass,the surface gravitational redshift and the Keplerian frequency for the traditional neutron star and the hyperon star matter within the relativistic mean field theory,using the GM1 and TM1 parameter sets by considering the two flavor symmetries of SU(6)and SU(3)combined with the observations of PSR J1614-2230,PSR J0348+0432,PSR J0030+0451,RX J0720.4-3125,and 1E 1207.4-5209.It is found that the existence of dark energy leads to the softened equations of the state of the traditional neutron star and the hyperon star.The radius of a fixed-mass traditional neutron star(or hyperon star)with dark energy becomes smaller,which leads to increased compactness.The existence of dark energy can also enhance the surface gravitational redshift and the Keplerian frequency of traditional neutron stars and hyperon stars.The growth of the Keplerian frequency may cause the spin rate to speed up,which may provide a possible way to understand and explain the pulsar glitch phenomenon.Specifically,we infer that the mass and the surface gravitational redshift of PSR J1748-2446ad without dark energy for the GM1(TM1)parameter set are 1.141 M_(☉)(1.309 M_(☉))and 0.095(0.105),respectively.The corresponding values for the GM1(TM1)parameter set are 0.901 M_(☉)(1.072M_(☉))and 0.079(0.091)if PSR J1748-2446ad contains dark energy withα=0.05.PSR J1748-2446ad may be a low-mass pulsar with a lower surface gravitational redshift under our selected models.展开更多
Sterile neutrinos can influence the evolution of the Universe,and thus cosmological observations can be used to detect them.Future gravitational-wave(GW)observations can precisely measure absolute cosmological distanc...Sterile neutrinos can influence the evolution of the Universe,and thus cosmological observations can be used to detect them.Future gravitational-wave(GW)observations can precisely measure absolute cosmological distances,helping to break parameter degeneracies generated by traditional cosmological observations.This advancement can lead to much tighter constraints on sterile neutrino parameters.This work provides a preliminary forecast for detecting sterile neutrinos using third-generation GW detectors in combination with future shortγ-ray burst observations from a THESEUS-like telescope,an approach not previously explored in the literature.Both massless and massive sterile neutrinos are considered within theΛCDM cosmology.We find that using GW data can greatly enhance the detection capability for massless sterile neutrinos,reaching 3σlevel.For massive sterile neutrinos,GW data can also greatly assist in improving the parameter constraints,but it seems that effective detection is still not feasible.展开更多
Relic gravitational waves(RGWs)from the early Universe carry crucial and fundamental cosmological information.Therefore,it is of extraordinary importance to investigate potential RGW signals in the data from observato...Relic gravitational waves(RGWs)from the early Universe carry crucial and fundamental cosmological information.Therefore,it is of extraordinary importance to investigate potential RGW signals in the data from observatories such as the LIGO-Virgo-KAGRA network.Here,focusing on typical RGWs from the inflation and the first-order phase transition(by sound waves and bubble collisions),effective and targeted deep learning neural networks are established to search for these RGW signals within the real LIGO data(O2,O3a and O3b).Through adjustment and adaptation processes,we develop suitable Convolutional Neural Networks(CNNs)to estimate the likelihood(characterized by quantitative values and distributions)that the focused RGW signals are present in the LIGO data.We find that if the constructed CNN properly estimates the parameters of the RGWs,it can determine with high accuracy(approximately 94%to 99%)whether the samples contain such RGW signals;otherwise,the likelihood provided by the CNN cannot be considered reliable.After testing a large amount of LIGO data,the findings show no evidence of RGWs from:1)inflation,2)sound waves,or 3)bubble collisions,as predicted by the focused theories.The results also provide upper limits of their GW spectral energy densities of h^(2)Ω_(gw)~10^(-5),respectively for parameter boundaries within 1)[β∈(-1.87,-1.85)×α∈(0.005,0.007)],2)[β/H_(pt)∈(0.02,0.16)×α∈(1,10)×T_(pt)∈(5*10^(9),10^(10))Gev],and 3)[β/H_(pt)∈(0.08,0.2)×α∈(1,10)×T_(pt)∈(5*10^(9),8*10^(10))Gev].In short,null results and upper limits are obtained,and the analysis suggests that our developed methods and neural networks to search for typical RGWs in the LIGO data are effective and reliable,providing a viable scheme for exploring possible RGWs from the early Universe and placing constraints on relevant cosmological theories.展开更多
The future space-borne gravitational wave(GW)detectors would provide a promising probe for the new physics beyond the standard model that admits the first-order phase transitions.The predictions for the GW background ...The future space-borne gravitational wave(GW)detectors would provide a promising probe for the new physics beyond the standard model that admits the first-order phase transitions.The predictions for the GW background vary sensitively among different concrete particle physics models but also share a large degeneracy in the model buildings,which motivates an effective model description on the phase transition based on different patterns of the electroweak symmetry breaking(EWSB).In this paper,using the scalar N-plet model as a demonstration,we propose an effective classification for three different patterns of EWSB:(1)radiative symmetry breaking with classical scale invariance,(2)the Higgs mechanism in a generic scalar extension,and(3)higher-dimensional operators.We conclude that a strong first-order phase transition could be realized for(1)and(2)with a small quartic coupling and a small isospin of an additional N-plet field for the light scalar field model with and without the classical scale invariance,and(3)with a large mixing coupling between scalar fields and a large isospin of the N-plet field for the heavy scalar field model.展开更多
The gravitational deflection of light signals restricted in the polar-axis plane of a moving Kerr–Newman(KN)black hole with a constant velocity along the polar axis is studied within the second post-Minkowskian(PM)ap...The gravitational deflection of light signals restricted in the polar-axis plane of a moving Kerr–Newman(KN)black hole with a constant velocity along the polar axis is studied within the second post-Minkowskian(PM)approximation.For this purpose,the Lorentz boosting technique is adopted to obtain the exact metric of a moving KN black hole with an arbitrary constant velocity in Kerr–Schild coordinates for the first time.Based on the weak field limit of the exact metric,we then derive the equations of motion of test particles constrained in the polaraxis plane of a moving KN source whose velocity is along the polar axis and collinear with its angular momentum.An iterative technique is utilized subsequently in the calculations of the null deflection angle up to the 2PM order caused by the moving lens,and this deflection angle is found to be spin-independent.Finally,we discuss the influence of the motion of the lens on the gravitational deflection and estimate the possibility of detecting this kinematical effect.Our work might be helpful for future astronomical observations.展开更多
The phenomenon that a clock at a higher gravitational potential ticks faster than one at a lower potential,also known as gravitational redshift,is one of the classical tests of Einstein’s theory of general relativity...The phenomenon that a clock at a higher gravitational potential ticks faster than one at a lower potential,also known as gravitational redshift,is one of the classical tests of Einstein’s theory of general relativity.Owing to their ultra-high accuracy and stability,state-of-the-art optical lattice clocks have enabled resolving the gravitational redshift with a millimeter-scale height difference.Further reducing the vertical inter-clock separation down to the sub-millimeter level and especially shortening the required measurement time may be achieved by employing spin squeezing.Here,we theoretically investigate the spin-squeezing-enhanced differential frequency comparison between two optical clocks within a lattice-trapped cloud of^(171)Yb atoms.The numerical results illustrate that for a sample of 10^(4)atoms,the atomic-collision-limited resolution of the vertical separation between two clocks can reach 0.48 mm,corresponding to a fractional gravitational redshift at the 10^(-20)level.In addition,the required averaging time may be reduced to less than one hundredth of that of conventional clocks with independent atoms.Our work opens a door to the future spin-squeezing-enhanced test of general relativity.展开更多
In weak field limits,we compute the deflection angle of a gravitational decoupling extended black hole(BH)solution.We obtained the Gaussian optical curvature by examining the null geodesic equations with the help of G...In weak field limits,we compute the deflection angle of a gravitational decoupling extended black hole(BH)solution.We obtained the Gaussian optical curvature by examining the null geodesic equations with the help of Gauss-Bonnet theorem(GBT).We also looked into the deflection angle of light by a black hole in weak field limits with the use of the Gibbons-Werner method.We verify the graphical behavior of the black hole after determining the deflection angle of light.Additionally,in the presence of the plasma medium,we also determine the deflection angle of the light and examine its graphical behavior.Furthermore,we compute the Einstein ring via gravitational decoupling extended black hole solution.We also compute the quasi-periodic oscillations and discuss their graphical behavior.展开更多
Based on the mass-energy equation of special relativity and the assumption of the helical motion of light speed in cosmic space,we have theoretically demonstrated the true implications of Planck’s physical quantities...Based on the mass-energy equation of special relativity and the assumption of the helical motion of light speed in cosmic space,we have theoretically demonstrated the true implications of Planck’s physical quantities:Planck length and time represent the step size and period of the helical motion of light speed in the earliest cosmic space following the Big Bang;Planck energy constitutes the minimum energy unit associated with this spatial helical motion;Planck mass is the mass derived from this minimum energy unit.In accordance with the expression of Planck time,we have derived the relationship formula between gravitational acceleration and the speed of light,thereby uncovering an inevitable intrinsic connection between the gravitational field and the electromagnetic field,and indicating that the four fundamental forces in the universe can be unified.Finally,through our spatial helical motion model,we computed the specific values of the four fundamental forces at the moment of strong nuclear force separation.The results reveal that they are in complete agreement with the theoretical calculation values or experimental values in modern physics and quantum mechanics,thereby providing an interesting hint for the unified field theories.展开更多
Extreme-mass-ratio inspiral(EMRI)signals pose significant challenges to gravitational wave(GW)data analysis,mainly owing to their highly complex waveforms and high-dimensional parameter space.Given their extended time...Extreme-mass-ratio inspiral(EMRI)signals pose significant challenges to gravitational wave(GW)data analysis,mainly owing to their highly complex waveforms and high-dimensional parameter space.Given their extended timescales of months to years and low signal-to-noise ratios,detecting and analyzing EMRIs with confidence generally relies on long-term observations.Besides the length of data,parameter estimation is particularly challenging due to non-local parameter degeneracies,arising from multiple local maxima,as well as flat regions and ridges inherent in the likelihood function.These factors lead to exceptionally high time complexity for parameter analysis based on traditional matched filtering and random sampling methods.To address these challenges,the present study explores a machine learning approach to Bayesian posterior estimation of EMRI signals,leveraging the recently developed flow matching technique based on ordinary differential equation neural networks.To our knowledge,this is also the first instance of applying continuous normalizing flows to EMRI analysis.Our approach demonstrates an increase in computational efficiency by several orders of magnitude compared to the traditional Markov chain Monte Carlo(MCMC)methods,while preserving the unbiasedness of results.However,we note that the posterior distributions generated by FMPE may exhibit broader uncertainty ranges than those obtained through full Bayesian sampling,requiring subsequent refinement via methods such as MCMC.Notably,when searching from large priors,our model rapidly approaches the true values while MCMC struggles to converge to the global maximum.Our findings highlight that machine learning has the potential to efficiently handle the vast EMRI parameter space of up to seventeen dimensions,offering new perspectives for advancing space-based GW detection and GW astronomy.展开更多
文摘In a recent article, we have corrected the traditional derivation of the Schwarzschild metric, thus obtaining the formulation of the correct Schwarzschild metric, which is different from the traditional Schwarzschild metric. Then, in another article by starting from this correct Schwarzschild metric, we have corrected also the Reissner-Nordstrøm, Kerr and Kerr-Newman metrics. On the other hand, in a third article, always by starting from this correct Schwarzschild metric, we have obtained the formulas of the correct gravitational potential and of the correct gravitational force in the case described by this metric. Now, in this article, by starting from these correct Reissner-Nordstrøm, Kerr and Kerr-Newman metrics and proceeding in a manner analogous to this third article, we obtain the formulas of the correct gravitational potential and of the correct gravitational force in the cases described by these metrics. Moreover, we analyze these correct results and their consequences. Finally, we propose some possible crucial experiments between the commonly accepted theory and the same theory corrected according to this article.
文摘The paper is devoted to the study of the gravitational collapse within the framework of the spherically symmetric problem in the Newton theory and general relativity on the basis of the pressure-free model of the continuum. In application to the Newton gravitation theory, the analysis consists of three stages. First, we assume that the gravitational force is determined by the initial sphere radius and constant density and does not change in the process of the sphere collapse. The obtained analytical solution allows us to find the collapse time in the first approximation. Second, we construct the step-by-step process in which the gravitational force at a given time moment depends on the current sphere radius and density. The obtained numerical solution specifies the collapse time depending on the number of steps. Third, we find the exact value of the collapse time which is the limit of the step-by-step solutions and study the collapse and the expansion processes in the Newton theory. In application to general relativity, we use the space model corresponding to the special four-dimensional space which is Euclidean with respect to space coordinates and Riemannian with respect to the time coordinate only. The obtained solution specifies two possible scenarios. First, sphere contraction results in the infinitely high density with the finite collapse time, which does not coincide with the conventional result corresponding to the Schwarzschild geometry. Second, sphere expansion with the velocity which increases with a distance from the sphere center and decreases with time.
文摘The discovery by the author of real magnetic charges and true anti-electrons in the atomic structures allowed him to establish that the gravitational field (GF) in reality is the vortex electromagnetic field. Depending on the vector conditions the gravitational fields can be either paragravitational (PGF) or ferrogravitational (FGF). Masses (atoms, nucleons, etc.) emitting PGF manifest so-called attraction to each other. In fact, this process is the pressing of atoms or nucleons to each other by the forces of gravitational “Dark energy”. Namely the gravitational “Dark energy” which is formed between the masses emitting PGF and compressing of nucleons in atomic nuclei is the main force factor determining the formation of nuclear forces. Masses that emit FGF are repelled from PGF sources, for example, from the Earth. The last gravitational manifestation, discovered by the author, this is of the effect of the gravitational levitation. The atomic shell and atomic nucleus are autonomous sources of gravitational field in atomic compositions. The gravitational fields emitted these sources, by its physical parameters, are different gravitational fields, what associated with differences in the magnitudes charges of magnetic and electric particles in their compositions. The noted differences in the parameters of the GF are of reason that in atoms the process of extrusion of foreign gravitational field from the region of given gravitational source is realized. This effect should be called the effect of intra-atomic gravitational shielding (IAGS). Within the framework of this effect the shell of the atom is a kind of gravitational “insulator” that prevents the PGF of the nucleons from leaving beyond of the atom. As result of the IAGS effect, the concentration PGF of nucleons is realized only in the region of the nucleus, which leads to an increase in nuclear forces. However, the resistance of the marked “insulator” is finite and if the critical voltage PGF on the nucleus is exceeded, the complete shielding of the nucleon fields by the atomic shell is broken. As result of the leakage of a part of the PGF of nucleons beyond the atom, the density of this field in the region of the nucleus decreases significantly, which leads to a weakening of the nuclear forces and often leads to radioactivity. The effect of gravitational shielding is directly related to such a well-known concept as the mass defect of the nucleus. It is the exclusion of the gravitational field formed by the nucleons in the composition of the atomic nucleus as a result of the full IAGS effect that creates the illusion of atomic mass defect.
文摘In the article ＂The Gravitational Force Quantum and its Value＂ [1 ], the author defined a gravitational force of the atomic unit （＂the Gravitational Force Quantum＂） as a gravitational force which exerts one atomic unit of the Earth＇s mass on l kilogram of a mass on the Earth＇s surface, and he calculated its value as： GFQEarth = 1.4958 × 10.54 N. In the present contribution, he extended the Gravitational Force Quantum concept to further Objects of the Solar Planetary System and for the Pluto. He calculated values of the GFQo on the analogous basis, i.e. of the mass and the standard acceleration of the gravity of individual objects and of the atomic unit of the mass. He received GFQo values for the Mercury 102.1427 × 1055N, the Venus 16,60012 × 10-55N, the Earth 14.97839 × l0-55 N, the Mars 52.91869 × 10-55N, the Jupiter 0.124391×1055 N, the Saturn 0.17929 ×1055N, the Uranus 0.945178 ×1055N, the Neptune 1.002845 × 10-55N, for the Pluto 458.9124 × 10-55N, and for the Sun 0.001257 × 10-55N, respectively. He multiplied the GFQo values by second power of the radii of the individual objects （O）, receiving values denoted as the ＂Elementary Gravitational Charge＂ （Go）. The Elementary Gravitational Charge represents a gravitational force of one atomic unit of mass in the （radius） distance of 1 meter. They were found of the same value： GMe= Gv = GE= GMa= Gj= Gs = Gp= GSun= 6.079675463 × 10-41N. The values were the same as the calculated one on the basis of the ＂classical＂ Newton＇s formula： FG = И × M × m / R2, for the gravitational force between the atomic unit mass and a mass of 1 kg at a distance of 1 meter, which value was calculated as G = 6.079675463 ×1041 N. The quantity of the Elementary Gravitational Charge can be supposed to be analogous to the Elementary （Electric） Charge （e =1.6021766208（98） × 10-19 C） quantity.
文摘The study by the author of magnetic scattering neutrons in the structures of ferrimagnets, as well as his experiments with the separation of magnetic charges in dipole pairs ±g in magnetic field, showed that fundamental magnetic particles (magnetic charges) are real structural components of atoms and substance. It is the magnetic poles, and not the moving electric charges are the direct sources of all magnetic fields and magnetic manifestations in Nature. Basic reasons of ignoring the magnetic fundamental particles by world physical theory, for almost 150 years, are the ultra-harsh confinement of these particles in substance which radically is different from the confinement electrons, as well as the vicious concept of the electric magnetism Maxwell. Rotating magnetic dipoles in conductors which are untwisted by electric current, are direct sources of the vortex magnetic field rot<em><strong>H</strong></em>. One should also expect the formation of a vortex electric field rot<em><strong>E </strong></em>forming by rotating electric dipoles which are untwisted by the current of magnetic charges. This article provides an experimental answer to the question: what field is formed around a conductor if joint direct currents of electric<em> <strong style="white-space:normal;"><em>J</em></strong></em><sub>e</sub> and magnetic<strong><em> J</em></strong><sub>g</sub> charges are passed through it? The author’s experiments have shown that in this case the vortex electromagnetic current is realized which manifests itself as the vortex electromagnetic (gravitational) field. It is possible to implement such a process, according to the results of the author’s research, exclusively in superconductors. The vector character of the gravitational field is in many respects similar to the vortex magnetic field which makes it possible to introduce such it states as paragravitation and ferrogravitation into representations. To create joint currents of electric and magnetic charges, the author used the inertial forces of these particles under conditions of acceleration and deceleration of the rotational motion of the closed lead superconductor. The result of this experiment was the gravitational, as it turned out later, the ferrogravitational field, which was detected by effect repulsion of trial cargos from the coil with a superconducting winding at the stage of its untwist. The latter process is defined by the author as an effect of the gravitational (ferrogravitational) levitation. The values of ferrogravitational (levitational) forces noted in this experiment were: 120 mg for a tungsten trial cargo and 50 and 25 mg for a lead cargo with an error of ±15 mg. The values of ferrogravitational (levitational) forces noted in this experiment are: 120 mg for from tungsten trial cargo and 50 and 25 mg for a cargo from lead, with an error of ±15 mg. The “anomaly” noted by the author in this study was in the absence of any absence of a gravitational effect on stage a braking of the coil. Probable cause of the noted “anomaly” is discussed in the Discussion of Results chapter.
文摘As is generally known, Newton＇s notion of universal gravitation surpassed various theories of particular gravities in the early modem age, as represented mainly by Kepler and Hooke. In his seminal work Hooke and the Law of Universal Gravitation： A Reappraisal of a Reappraisal Richard S. Westfall argues that Hooke could not reach beyond the concept of spatially bounded particular gravities, as he deployed the method of analogy between the material principle of congruity and incongruity and the extension of gravitational spheres and their action at a distance. However, the doctrine of universal gravitation does not exclude the nature of particular gravities; it is predicated on the notion of an infinite expansion of individual-gravitational spheres and their uniform nature, namely the mutual and centripetal attraction. In my treatise 1 attempt to reinvestigate the nature and structure of gravitation, as established historically in the framework of Newtonian Classical Mechanics, by a method of structural intuition. It examines how the structural intuition, as represented in the celestial-mechanical intuitions of Hooke and Kepler, could unfold into an innovative process within the context of early modem mechanical philosophy, attaining thus a historical siglaificance and legitimacy as against the prevailing Newtonian method of geometric-mathematical axiomatization of mechanical principles. It also explores the actual demonstrative features of the tidal phenomenon with regard to its lunar- and solar-gravitational causation, which has been considered to date to be an important piece of empirical evidence for the theory of universal gravitation.
文摘The study of the effect of the gravitational field on the photons, based on the hypothesis of the absolute reference system, demonstrates the origin of the gravitational force. By studying the propagation of a photon in the gravitational field the change in the estimation of time is determined, resulting from the use of a clock that is affected by the gravitational field. It is proved that in all known experiments, which were carried out in order to confirm the general theory of relativity, the results based on the hypothesis of an absolute reference system agree with the corresponding results of the general theory of relativity, except for the result of the deflection of light in the gravitational field of the sun, where the experimental results confirm the hypothesis of the absolute reference system.
文摘Exoplanet imaging using the solar gravitational lens is an enticing prospect.The fundamental physical properties of the lens,including its angular resolution and light amplification,promise exceptional capabilities.These expectations,however,are tempered by the realization of numerous challenges,including imperfections of the lens itself,noise sources,the properties of the imaging target and difficult technical issues.We discuss,in particular,a subject not previously addressed,the impact of temporally varying surface features,notably a variable cloud cover,obscuring the target exoplanet.This has a substantial detrimental effect on image recovery,leading to our cautious assessment of the practical feasibility of using the Sun’s gravitational field as an effective telescope.
文摘The Newtonian gravitational constant G is one of the most important fundamental constants of nature, but still remains resistant to the standard model of physics and disconnected from quantum theory. During the past >100 years, hundreds of G values have been measured to be ranging around 6.66 to 6.7559 × 10−11 m3·kg−1·s−2 using macroscopic masses. More recently, however, a G value ((6.04 ± 0.06) × 10−11 m3·kg−1·s−2) measured using millimetre-sized masses shows significant deviation (by ~9%) from the reference G value, which the authors explained is resulted from “the known systematic uncertainties”. However, based on the observation of historical G values and the protocol of the millimetre-sized masses based experiment, here we proposed a theory that this deviation is not from “systematic uncertainties” but actually G will rapidly decrease when masses sphere diameter is less than 0.02 metres. Moreover, this theory predicted the G value will be 5.96 × 10−11 m3·kg−1·s−2 between masses whose diameter are 2 millimetres (0.002 metres), which matches the measured G value very well.
文摘We present a theoretical model for detecting axions from neutron stars in a QCD phase of quark matter. The axions would be produced from a quark-antiquark pair uu¯or dd¯, in loop(s) involving gluons. The chiral anomaly of QCD and the spontaneously broken symmetry are invoked to explain the non-conservation of the axion current. From the coupling form factors, the axion emissivities ϵacan be derived, from which fluxes can be determined. We predict a photon flux, which may be detectable by Fermi LAT, and limits on the QCD mass ma. In this model, axions decay to gamma rays in a 2-photon vertex. We may determine the expected fluxes from the theoretical emissivity. The sensitivity curve from the Fermi Large Area Telescope (Fermi LAT) would allow axion mass constraints for neutron stars as low as ma≤10−14eV 95% C.L. Axions could thus be detectable in gamma rays for neutron stars as distant as 100 kpc. A signal from LIGO GWS 170817 could be placed from the NS-NS merger, which gives an upper limit of ma≤10−10eV.
基金supported by the Hunan Provincial Natural Science Foundation(No.2016JJ3034).
文摘Einstein aimed to find a unified theoretical model to explain various interactions in nature,and the relationship between gravitational and electric fields was particularly important.For the first time,this paper provides the internal relationship equations of the electric and magnetic fields.Further,the relationship between the magnetic and gravity fields is analyzed,and the relationship equations of the electric,magnetic,and gravity fields are established.On this basis,a general formula for calculating the radius of charged particles is derived.Simultaneously,we also discussed and made predictions on black holes,providing convenience for future research and experimental detection.
基金partially funded by the Horizontal Scientific Research Project of the National Astronomical Observatories of CAS(Grant No.E0900501)and the Theoretical Fundamental Research Special Project of the Changchun Observatory,National Astronomical Observatories,CAS(Grant No.Y990000205)。
文摘Research on the properties of neutron stars with dark energy is a particularly interesting yet unresolved problem in astrophysics.We analyze the influence of dark energy on the equation of state,the maximum mass,the surface gravitational redshift and the Keplerian frequency for the traditional neutron star and the hyperon star matter within the relativistic mean field theory,using the GM1 and TM1 parameter sets by considering the two flavor symmetries of SU(6)and SU(3)combined with the observations of PSR J1614-2230,PSR J0348+0432,PSR J0030+0451,RX J0720.4-3125,and 1E 1207.4-5209.It is found that the existence of dark energy leads to the softened equations of the state of the traditional neutron star and the hyperon star.The radius of a fixed-mass traditional neutron star(or hyperon star)with dark energy becomes smaller,which leads to increased compactness.The existence of dark energy can also enhance the surface gravitational redshift and the Keplerian frequency of traditional neutron stars and hyperon stars.The growth of the Keplerian frequency may cause the spin rate to speed up,which may provide a possible way to understand and explain the pulsar glitch phenomenon.Specifically,we infer that the mass and the surface gravitational redshift of PSR J1748-2446ad without dark energy for the GM1(TM1)parameter set are 1.141 M_(☉)(1.309 M_(☉))and 0.095(0.105),respectively.The corresponding values for the GM1(TM1)parameter set are 0.901 M_(☉)(1.072M_(☉))and 0.079(0.091)if PSR J1748-2446ad contains dark energy withα=0.05.PSR J1748-2446ad may be a low-mass pulsar with a lower surface gravitational redshift under our selected models.
基金supported by the National Natural Science Foundation of China under Grant Nos.12305069,11947022,12473001,11975072,11875102,and 11835009the National SKA Program of China under Grants Nos.2022SKA0110200 and 2022SKA0110203+1 种基金the Program of the Education Department of Liaoning Province under Grant No.JYTMS20231695the National 111 Project under Grant No.B16009。
文摘Sterile neutrinos can influence the evolution of the Universe,and thus cosmological observations can be used to detect them.Future gravitational-wave(GW)observations can precisely measure absolute cosmological distances,helping to break parameter degeneracies generated by traditional cosmological observations.This advancement can lead to much tighter constraints on sterile neutrino parameters.This work provides a preliminary forecast for detecting sterile neutrinos using third-generation GW detectors in combination with future shortγ-ray burst observations from a THESEUS-like telescope,an approach not previously explored in the literature.Both massless and massive sterile neutrinos are considered within theΛCDM cosmology.We find that using GW data can greatly enhance the detection capability for massless sterile neutrinos,reaching 3σlevel.For massive sterile neutrinos,GW data can also greatly assist in improving the parameter constraints,but it seems that effective detection is still not feasible.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.11605015,12347101 and 12147102the Natural Scienceof Chongqing under Grant No.cstc2020jcyjmsxm X0944the Research Funds for the Central Universities under Grant No.2022CDJXY-002。
文摘Relic gravitational waves(RGWs)from the early Universe carry crucial and fundamental cosmological information.Therefore,it is of extraordinary importance to investigate potential RGW signals in the data from observatories such as the LIGO-Virgo-KAGRA network.Here,focusing on typical RGWs from the inflation and the first-order phase transition(by sound waves and bubble collisions),effective and targeted deep learning neural networks are established to search for these RGW signals within the real LIGO data(O2,O3a and O3b).Through adjustment and adaptation processes,we develop suitable Convolutional Neural Networks(CNNs)to estimate the likelihood(characterized by quantitative values and distributions)that the focused RGW signals are present in the LIGO data.We find that if the constructed CNN properly estimates the parameters of the RGWs,it can determine with high accuracy(approximately 94%to 99%)whether the samples contain such RGW signals;otherwise,the likelihood provided by the CNN cannot be considered reliable.After testing a large amount of LIGO data,the findings show no evidence of RGWs from:1)inflation,2)sound waves,or 3)bubble collisions,as predicted by the focused theories.The results also provide upper limits of their GW spectral energy densities of h^(2)Ω_(gw)~10^(-5),respectively for parameter boundaries within 1)[β∈(-1.87,-1.85)×α∈(0.005,0.007)],2)[β/H_(pt)∈(0.02,0.16)×α∈(1,10)×T_(pt)∈(5*10^(9),10^(10))Gev],and 3)[β/H_(pt)∈(0.08,0.2)×α∈(1,10)×T_(pt)∈(5*10^(9),8*10^(10))Gev].In short,null results and upper limits are obtained,and the analysis suggests that our developed methods and neural networks to search for typical RGWs in the LIGO data are effective and reliable,providing a viable scheme for exploring possible RGWs from the early Universe and placing constraints on relevant cosmological theories.
基金supported by the National Key Research and Development Program of China under Grant Nos.2021YFC2203004,2021YFA0718304,2020YFC2201501RGC is supported by the National Natural Science Foundation of China under Grants Nos.11947302,11991052,11690022,11821505 and 11851302+8 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences(CAS)under Grant Nos.XDB23030100 and XDA15020701the Key Research Program of the CAS under Grant No.XDPB15the Key Research Program of Frontier Sciences of CAS.SJW is supported by the National Key Research and Development Program of China under Grant Nos.2021YFC2203004 and 2021YFA0718304the National Natural Science Foundation of China under Grant Nos.12422502 and 12105344the China Manned Space Project under Grant No.CMS-CSST-2021-B01JHY is supported by the National Science Foundation of China under Grant Nos.12022514,11875003 and 12047503the National Key Research and Development Program of China under Grant Nos.2020YFC2201501 and 2021YFA0718304the CAS Project for Young Scientists in Basic Research under Grant No.YSBR-006the Key Research Program of the CAS under Grant No.XDPB15.
文摘The future space-borne gravitational wave(GW)detectors would provide a promising probe for the new physics beyond the standard model that admits the first-order phase transitions.The predictions for the GW background vary sensitively among different concrete particle physics models but also share a large degeneracy in the model buildings,which motivates an effective model description on the phase transition based on different patterns of the electroweak symmetry breaking(EWSB).In this paper,using the scalar N-plet model as a demonstration,we propose an effective classification for three different patterns of EWSB:(1)radiative symmetry breaking with classical scale invariance,(2)the Higgs mechanism in a generic scalar extension,and(3)higher-dimensional operators.We conclude that a strong first-order phase transition could be realized for(1)and(2)with a small quartic coupling and a small isospin of an additional N-plet field for the light scalar field model with and without the classical scale invariance,and(3)with a large mixing coupling between scalar fields and a large isospin of the N-plet field for the heavy scalar field model.
基金supported in part by the National Natural Science Foundation of China(grant Nos.11973025,12205139,12303079,12475057,and 12481540180)the Natural Science Foundation of Hunan Province(grant No.2022JJ40347)。
文摘The gravitational deflection of light signals restricted in the polar-axis plane of a moving Kerr–Newman(KN)black hole with a constant velocity along the polar axis is studied within the second post-Minkowskian(PM)approximation.For this purpose,the Lorentz boosting technique is adopted to obtain the exact metric of a moving KN black hole with an arbitrary constant velocity in Kerr–Schild coordinates for the first time.Based on the weak field limit of the exact metric,we then derive the equations of motion of test particles constrained in the polaraxis plane of a moving KN source whose velocity is along the polar axis and collinear with its angular momentum.An iterative technique is utilized subsequently in the calculations of the null deflection angle up to the 2PM order caused by the moving lens,and this deflection angle is found to be spin-independent.Finally,we discuss the influence of the motion of the lens on the gravitational deflection and estimate the possibility of detecting this kinematical effect.Our work might be helpful for future astronomical observations.
基金supported by CAS Project for Young Scientists in Basic Research(Grant No.YSBR-085)the National Time Service Center(Grant No.E239SC1101)+1 种基金Innovation Program for Quantum Science and Technology(Grant No.2021ZD0303200)China Postdoctoral Science Foundation(Grant No.BX2021020).
文摘The phenomenon that a clock at a higher gravitational potential ticks faster than one at a lower potential,also known as gravitational redshift,is one of the classical tests of Einstein’s theory of general relativity.Owing to their ultra-high accuracy and stability,state-of-the-art optical lattice clocks have enabled resolving the gravitational redshift with a millimeter-scale height difference.Further reducing the vertical inter-clock separation down to the sub-millimeter level and especially shortening the required measurement time may be achieved by employing spin squeezing.Here,we theoretically investigate the spin-squeezing-enhanced differential frequency comparison between two optical clocks within a lattice-trapped cloud of^(171)Yb atoms.The numerical results illustrate that for a sample of 10^(4)atoms,the atomic-collision-limited resolution of the vertical separation between two clocks can reach 0.48 mm,corresponding to a fractional gravitational redshift at the 10^(-20)level.In addition,the required averaging time may be reduced to less than one hundredth of that of conventional clocks with independent atoms.Our work opens a door to the future spin-squeezing-enhanced test of general relativity.
基金funded by the National Natural Science Foundation of China under Grant No.11975145。
文摘In weak field limits,we compute the deflection angle of a gravitational decoupling extended black hole(BH)solution.We obtained the Gaussian optical curvature by examining the null geodesic equations with the help of Gauss-Bonnet theorem(GBT).We also looked into the deflection angle of light by a black hole in weak field limits with the use of the Gibbons-Werner method.We verify the graphical behavior of the black hole after determining the deflection angle of light.Additionally,in the presence of the plasma medium,we also determine the deflection angle of the light and examine its graphical behavior.Furthermore,we compute the Einstein ring via gravitational decoupling extended black hole solution.We also compute the quasi-periodic oscillations and discuss their graphical behavior.
文摘Based on the mass-energy equation of special relativity and the assumption of the helical motion of light speed in cosmic space,we have theoretically demonstrated the true implications of Planck’s physical quantities:Planck length and time represent the step size and period of the helical motion of light speed in the earliest cosmic space following the Big Bang;Planck energy constitutes the minimum energy unit associated with this spatial helical motion;Planck mass is the mass derived from this minimum energy unit.In accordance with the expression of Planck time,we have derived the relationship formula between gravitational acceleration and the speed of light,thereby uncovering an inevitable intrinsic connection between the gravitational field and the electromagnetic field,and indicating that the four fundamental forces in the universe can be unified.Finally,through our spatial helical motion model,we computed the specific values of the four fundamental forces at the moment of strong nuclear force separation.The results reveal that they are in complete agreement with the theoretical calculation values or experimental values in modern physics and quantum mechanics,thereby providing an interesting hint for the unified field theories.
基金supported by the National Key Research and Development Program of China(Grant Nos.2021YFC2201901,2021YFC2203004,2020YFC2200100 and 2021YFC2201903)International Partnership Program of the Chinese Academy of Sciences(Grant No.025GJHZ2023106GC)+4 种基金the financial support from Brazilian agencies Funda??o de AmparoàPesquisa do Estado de S?o Paulo(FAPESP)Funda??o de Amparoà Pesquisa do Estado do Rio Grande do Sul(FAPERGS)Fundacao de Amparoà Pesquisa do Estado do Rio de Janeiro(FAPERJ)Conselho Nacional de Desenvolvimento Científico e Tecnológico(CNPq)Coordenacao de Aperfeicoamento de Pessoal de Nível Superior(CAPES)。
文摘Extreme-mass-ratio inspiral(EMRI)signals pose significant challenges to gravitational wave(GW)data analysis,mainly owing to their highly complex waveforms and high-dimensional parameter space.Given their extended timescales of months to years and low signal-to-noise ratios,detecting and analyzing EMRIs with confidence generally relies on long-term observations.Besides the length of data,parameter estimation is particularly challenging due to non-local parameter degeneracies,arising from multiple local maxima,as well as flat regions and ridges inherent in the likelihood function.These factors lead to exceptionally high time complexity for parameter analysis based on traditional matched filtering and random sampling methods.To address these challenges,the present study explores a machine learning approach to Bayesian posterior estimation of EMRI signals,leveraging the recently developed flow matching technique based on ordinary differential equation neural networks.To our knowledge,this is also the first instance of applying continuous normalizing flows to EMRI analysis.Our approach demonstrates an increase in computational efficiency by several orders of magnitude compared to the traditional Markov chain Monte Carlo(MCMC)methods,while preserving the unbiasedness of results.However,we note that the posterior distributions generated by FMPE may exhibit broader uncertainty ranges than those obtained through full Bayesian sampling,requiring subsequent refinement via methods such as MCMC.Notably,when searching from large priors,our model rapidly approaches the true values while MCMC struggles to converge to the global maximum.Our findings highlight that machine learning has the potential to efficiently handle the vast EMRI parameter space of up to seventeen dimensions,offering new perspectives for advancing space-based GW detection and GW astronomy.
