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
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
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
We simulate the gravitational redshift of quantum matter waves with a long de Broglie wavelength by tracing particle beams along geodesics,when they propagate within the rotation plane of binary black holes.The angula...We simulate the gravitational redshift of quantum matter waves with a long de Broglie wavelength by tracing particle beams along geodesics,when they propagate within the rotation plane of binary black holes.The angular momentum of the binary black hole causes an asymmetric gravitational redshift distribution around the two black holes.The gravitational redshift changes the frequency of quantum matter waves and their wavelength,resulting in the different interference patterns of quantum matter waves with respect to different wavelengths.The interference pattern demonstrates strong contrast intensity and spatial order with respect to different wavelengths and the rotational angle of the binary black hole.A bright semicircular arc emerges from the interference pattern to bridge the two black holes,when they rotate to certain angles,which provides a theoretical understanding on the gravitational lensing effect of quantum matter waves.展开更多
In this paper,we investigate the optical properties of a non-rotating charged black hole(BH)in the Einstein-Maxwell-scalar(EMS)theory,together with a plasma medium.We first consider the photon sphere and shadow radius...In this paper,we investigate the optical properties of a non-rotating charged black hole(BH)in the Einstein-Maxwell-scalar(EMS)theory,together with a plasma medium.We first consider the photon sphere and shadow radius under the impact of the plasma medium existing in the environment surrounding the BH in the EMS theory.We show that the radius of the photon sphere and the BH shadow decrease under the influence of the parameterβ.We further study gravitational weak lensing in detail by adapting general methods and derive the light ray's deflection angle around the BH together with the plasma environment.It is found that for uniform plasma,the deflection angle increases with the rise of the plasma parameter,whereas it decreases with the increase of the plasma parameter for non-uniform plasma.Besides,we also study the magnification of image brightness.展开更多
This paper presents an analysis of an equilateral triangular array formation initialization for space-based gravitational wave observatory(GWO)near Lagrange points in the circular-restricted three-body problem.A stabl...This paper presents an analysis of an equilateral triangular array formation initialization for space-based gravitational wave observatory(GWO)near Lagrange points in the circular-restricted three-body problem.A stable configuration is essential for the continuous observation of gravitational waves(GWs).However,the motion near the collinear libration points is highly unstable.This problem is examined by output regulation theory.Using the tracking aspect,the equilateral triangular array formation is established in two periods and the fuel consumption is calculated.Furthermore,the natural evolution of the formation without control input is analyzed,and the effective stability duration is quantified to determine the timing of control interventions.Finally,to observe the GWs in same direction with different frequency bands,scale reconfiguration is employed.展开更多
The gravitational wave background(GWB) produced by extreme-mass-ratio inspirals(EMRIs) serves as a powerful tool for probing the astrophysical and dynamical processes in galactic centers. EMRI systems are a primary ta...The gravitational wave background(GWB) produced by extreme-mass-ratio inspirals(EMRIs) serves as a powerful tool for probing the astrophysical and dynamical processes in galactic centers. EMRI systems are a primary target for the space-based detector laser interferometer space antenna due to their long-lived signals and high signal-to-noise ratios. This study explores the statistical properties of the GWB from EMRI, focusing on the calculation methods for the GWB, the astrophysical distribution of EMRI sources, and the influence of key parameters, including the spin of supermassive black holes(SMBHs) and the masses of compact objects(COs). By analyzing these factors, we determine the distribution range of the characteristic strain of the GWB from EMRIs. We find that the final eccentricity distributions appear to have negligible effect on the intensity of the GWB due to rapid circularization before they become detectable and the spin of the SMBH enhances the gravitational wave characteristic strain by approximately 1% compared to cases without spin effects. The masses of COs can also significantly affect the characteristic strain of the GWB from EMRIs, with black hole as CO producing a gravitational wave signal intensity that is approximately one order of magnitude higher compared to cases where neutron star or white dwarf are the COs.展开更多
The Tian Qin space-borne gravitational wave detector will orbit at an altitude of1.0×10^(5)km with an arm length of 1.7×10^(5)km,structured in an equilateral triangular satellite formation.The Tian Qin proje...The Tian Qin space-borne gravitational wave detector will orbit at an altitude of1.0×10^(5)km with an arm length of 1.7×10^(5)km,structured in an equilateral triangular satellite formation.The Tian Qin project delineates detailed requirements for orbit determination during both the launch phase and subsequent scientific experimentation.This paper pioneers the investigation of Precise Orbit Determination(POD)for Tian Qin utilizing the third generation of Bei Dou global navigation satellite system(BDS-3)Inter-Satellite Link(ISL)through simulation.By analyzing the visibility,the feasibility of using BDS-3 ISLs for Tian Qin POD is explored.Furthermore,a refined Solar Radiation Pressure(SRP)model is developed,and the POD accuracy of Tian Qin is assessed,considering factors such as arc length,ranging intervals,and error sources.The results indicate the following:(A)Visibility between Tian Qin and BDS-3 satellites is intermittent,with an average of 10.6 BDS-3 satellites visible to Tian Qin,and the average Root Mean Square(RMS)-value of Position Dilution of Precision(PDOP)for Tian Qin is 48.13.(B)POD accuracy improves with shorter ranging intervals.(C)The error in ephemeris is the dominant factor affecting the POD accuracy.(D)The establishment of three links between Tian Qin and the BDS-3 satellites satisfies the POD requirements of Tian Qin.With a ranging interval of 600 s and over a 7-day arc,the average three-Dimensional(3D)position accuracy of the three Tian Qin satellites is 1.35 m,while the 3D velocity accuracy is 0.08 mm/s.展开更多
The gravitational curvatures(GC,the third-order derivatives of the gravitational potential)in gravity field modeling are gaining increased interest in geosciences.The crustal effects of the GC and Moho variation sense...The gravitational curvatures(GC,the third-order derivatives of the gravitational potential)in gravity field modeling are gaining increased interest in geosciences.The crustal effects of the GC and Moho variation sensed by the GC are not fully evaluated for the current study.In this contribution,the effects of the GC induced by topographic and anomalous crustal masses are investigated based on ETOPO1 and CRUST1.0 models using the tesseroids.By adopting the gravitational stripping correction,the residual GC sensed by the CRUST1.0 Moho depths are presented globally to examine whether the GC can sense crustal mass anomalies at the satellite altitude of 260 km.The spatial analysis using the Pearson correlations coefficient(PCC)between the residual GC and the CRUST1.0 Moho depths is performed.Among the 10 residual GC functionals,the PCC value of the residual radial-radial-radial componentδT^(res)_(zzz)is largest with 0.31,where this value is highly dependent on the spectral content removed from the EGM2008,e.g.signals assumed to relate to deeper mass anomalies.Numerical experiments show that with the increased order of the derivatives up to third-order,the fineness level of different global Moho sensed crustal mass anomalies increases correspondingly.Taking the Tibetan plateau for example,the values of theδT^(res)_(zzz)can better reveal the detailed features of the Tibetan plateau’s Moho depth than these of the lower-order residual radial functionals(i.e.disturbing potentialδTres,disturbing radial gravity vectorδT^(res)_(z),and disturbing radial-radial gravity gradient tensorδT^(res)_(zz)),especially for the Qaidam,Sichuan,Tarim,and Turpan basins.Numerical results over the Himalayan region demonstrate that the GC componentδT^(res)^(z)has some potential in geophysical inversion.These residual GC functionals would help to get a better knowledge of the internal structures of the Earth and other planetary objects.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.
文摘We simulate the gravitational redshift of quantum matter waves with a long de Broglie wavelength by tracing particle beams along geodesics,when they propagate within the rotation plane of binary black holes.The angular momentum of the binary black hole causes an asymmetric gravitational redshift distribution around the two black holes.The gravitational redshift changes the frequency of quantum matter waves and their wavelength,resulting in the different interference patterns of quantum matter waves with respect to different wavelengths.The interference pattern demonstrates strong contrast intensity and spatial order with respect to different wavelengths and the rotational angle of the binary black hole.A bright semicircular arc emerges from the interference pattern to bridge the two black holes,when they rotate to certain angles,which provides a theoretical understanding on the gravitational lensing effect of quantum matter waves.
基金supported by the National Natural Science Foundation of China under Grant No.11675143the National Key Research and Development Program of China under Grant No.2020YFC2201503。
文摘In this paper,we investigate the optical properties of a non-rotating charged black hole(BH)in the Einstein-Maxwell-scalar(EMS)theory,together with a plasma medium.We first consider the photon sphere and shadow radius under the impact of the plasma medium existing in the environment surrounding the BH in the EMS theory.We show that the radius of the photon sphere and the BH shadow decrease under the influence of the parameterβ.We further study gravitational weak lensing in detail by adapting general methods and derive the light ray's deflection angle around the BH together with the plasma environment.It is found that for uniform plasma,the deflection angle increases with the rise of the plasma parameter,whereas it decreases with the increase of the plasma parameter for non-uniform plasma.Besides,we also study the magnification of image brightness.
基金supported by the China Scholarship Council(CSC)(No.202206290131)。
文摘This paper presents an analysis of an equilateral triangular array formation initialization for space-based gravitational wave observatory(GWO)near Lagrange points in the circular-restricted three-body problem.A stable configuration is essential for the continuous observation of gravitational waves(GWs).However,the motion near the collinear libration points is highly unstable.This problem is examined by output regulation theory.Using the tracking aspect,the equilateral triangular array formation is established in two periods and the fuel consumption is calculated.Furthermore,the natural evolution of the formation without control input is analyzed,and the effective stability duration is quantified to determine the timing of control interventions.Finally,to observe the GWs in same direction with different frequency bands,scale reconfiguration is employed.
基金supported by the National Key R&D Program of China (Grant No. 2020YFC2201400)。
文摘The gravitational wave background(GWB) produced by extreme-mass-ratio inspirals(EMRIs) serves as a powerful tool for probing the astrophysical and dynamical processes in galactic centers. EMRI systems are a primary target for the space-based detector laser interferometer space antenna due to their long-lived signals and high signal-to-noise ratios. This study explores the statistical properties of the GWB from EMRI, focusing on the calculation methods for the GWB, the astrophysical distribution of EMRI sources, and the influence of key parameters, including the spin of supermassive black holes(SMBHs) and the masses of compact objects(COs). By analyzing these factors, we determine the distribution range of the characteristic strain of the GWB from EMRIs. We find that the final eccentricity distributions appear to have negligible effect on the intensity of the GWB due to rapid circularization before they become detectable and the spin of the SMBH enhances the gravitational wave characteristic strain by approximately 1% compared to cases without spin effects. The masses of COs can also significantly affect the characteristic strain of the GWB from EMRIs, with black hole as CO producing a gravitational wave signal intensity that is approximately one order of magnitude higher compared to cases where neutron star or white dwarf are the COs.
基金co-supported by the Guangdong Major Project of Basic and Applied Basic Research,China(No.2019B030302001)the Guangdong Basic and Applied Basic Research Foundation,China(No.2022A1515110236)the Fundamental Research Funds for the Central Universities,Sun Yat-Sen University,China(No.23xkjc001)。
文摘The Tian Qin space-borne gravitational wave detector will orbit at an altitude of1.0×10^(5)km with an arm length of 1.7×10^(5)km,structured in an equilateral triangular satellite formation.The Tian Qin project delineates detailed requirements for orbit determination during both the launch phase and subsequent scientific experimentation.This paper pioneers the investigation of Precise Orbit Determination(POD)for Tian Qin utilizing the third generation of Bei Dou global navigation satellite system(BDS-3)Inter-Satellite Link(ISL)through simulation.By analyzing the visibility,the feasibility of using BDS-3 ISLs for Tian Qin POD is explored.Furthermore,a refined Solar Radiation Pressure(SRP)model is developed,and the POD accuracy of Tian Qin is assessed,considering factors such as arc length,ranging intervals,and error sources.The results indicate the following:(A)Visibility between Tian Qin and BDS-3 satellites is intermittent,with an average of 10.6 BDS-3 satellites visible to Tian Qin,and the average Root Mean Square(RMS)-value of Position Dilution of Precision(PDOP)for Tian Qin is 48.13.(B)POD accuracy improves with shorter ranging intervals.(C)The error in ephemeris is the dominant factor affecting the POD accuracy.(D)The establishment of three links between Tian Qin and the BDS-3 satellites satisfies the POD requirements of Tian Qin.With a ranging interval of 600 s and over a 7-day arc,the average three-Dimensional(3D)position accuracy of the three Tian Qin satellites is 1.35 m,while the 3D velocity accuracy is 0.08 mm/s.
基金supported by National Natural Science Foundation of China[Grant Nos.42030105,41721003,41804012,41631072,41874023].
文摘The gravitational curvatures(GC,the third-order derivatives of the gravitational potential)in gravity field modeling are gaining increased interest in geosciences.The crustal effects of the GC and Moho variation sensed by the GC are not fully evaluated for the current study.In this contribution,the effects of the GC induced by topographic and anomalous crustal masses are investigated based on ETOPO1 and CRUST1.0 models using the tesseroids.By adopting the gravitational stripping correction,the residual GC sensed by the CRUST1.0 Moho depths are presented globally to examine whether the GC can sense crustal mass anomalies at the satellite altitude of 260 km.The spatial analysis using the Pearson correlations coefficient(PCC)between the residual GC and the CRUST1.0 Moho depths is performed.Among the 10 residual GC functionals,the PCC value of the residual radial-radial-radial componentδT^(res)_(zzz)is largest with 0.31,where this value is highly dependent on the spectral content removed from the EGM2008,e.g.signals assumed to relate to deeper mass anomalies.Numerical experiments show that with the increased order of the derivatives up to third-order,the fineness level of different global Moho sensed crustal mass anomalies increases correspondingly.Taking the Tibetan plateau for example,the values of theδT^(res)_(zzz)can better reveal the detailed features of the Tibetan plateau’s Moho depth than these of the lower-order residual radial functionals(i.e.disturbing potentialδTres,disturbing radial gravity vectorδT^(res)_(z),and disturbing radial-radial gravity gradient tensorδT^(res)_(zz)),especially for the Qaidam,Sichuan,Tarim,and Turpan basins.Numerical results over the Himalayan region demonstrate that the GC componentδT^(res)^(z)has some potential in geophysical inversion.These residual GC functionals would help to get a better knowledge of the internal structures of the Earth and other planetary objects.
