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
An association rules mining method based on semantic relativity is proposed to solve the problem that there are more candidate item sets and higher time complexity in traditional association rules mining.Semantic rela...An association rules mining method based on semantic relativity is proposed to solve the problem that there are more candidate item sets and higher time complexity in traditional association rules mining.Semantic relativity of ontology concepts is used to describe complicated relationships of domains in the method.Candidate item sets with less semantic relativity are filtered to reduce the number of candidate item sets in association rules mining.An ontology hierarchy relationship is regarded as a directed acyclic graph rather than a hierarchy tree in the semantic relativity computation.Not only direct hierarchy relationships,but also non-direct hierarchy relationships and other typical semantic relationships are taken into account.Experimental results show that the proposed method can reduce the number of candidate item sets effectively and improve the efficiency of association rules mining.展开更多
Sapir-Whorf Hypothesis is controversial, but the Linguistic Relativity is universally accepted by scholars. Through ana lyzing the causes of the mistakes that students often make during English learning and the relati...Sapir-Whorf Hypothesis is controversial, but the Linguistic Relativity is universally accepted by scholars. Through ana lyzing the causes of the mistakes that students often make during English learning and the relationship among thoughts, cultures and languages, this paper argues that language can influence people's thoughts and people's thoughts can influence the acquisi tion of a second language.展开更多
Since the special relativity can be viewed as the physics in an inverse Wick rotation of four-dimensional （4D） Euclid space, which is at almost equal footing with the 4D Riemann/Lobachevski space, there should be im...Since the special relativity can be viewed as the physics in an inverse Wick rotation of four-dimensional （4D） Euclid space, which is at almost equal footing with the 4D Riemann/Lobachevski space, there should be important physics in the inverse Wick rotation of 4D Riemann/Lobachevski space. Thus, there are three kinds of special relativity in de Sitter（dS）/Minkowski/anti-de Sitter（AdS） space at almost equal footing, respectively. There is an instanton tunnelling scenario in the Riemann-de Sitter case that may explain why A be positive and link with the multiverse.展开更多
We discuss one-dimensional Dirac oscillator, by using the concept doubly special relativity. We calculate the energy spectrum by using the concept doubly special relativity. Then, we derive another representation that...We discuss one-dimensional Dirac oscillator, by using the concept doubly special relativity. We calculate the energy spectrum by using the concept doubly special relativity. Then, we derive another representation that the coordinate operator remains unchanged at the high energy while the momentum operator is deformed at the high energy so that it may be bounded from the above. Actually, we study the Dirac oscillator by using of the generalized uncertainty principle version and the concept doubly special relativity.展开更多
In this work, we discuss the possibility to classify relativity in accordance with the classification of second order partial differential equations that have been applied into the formulation of physical laws in phys...In this work, we discuss the possibility to classify relativity in accordance with the classification of second order partial differential equations that have been applied into the formulation of physical laws in physics. In mathematics, since second order partial differential equations can be classified into hyperbolic, elliptic or parabolic type, therefore we show that it is also possible to classify relativity accordingly into hyperbolic, elliptic or parabolic type by establishing coordinate transformations that preserve the forms of these second order partial differential equations. The coordinate transformation that preserves the form of the hyperbolic equation is the Lorentz transformation and the associated space is the hyperbolic, or pseudo-Euclidean, relativistic spacetime. Typical equations in physics that comply with hyperbolic relativity are Maxwell and Dirac equations. The coordinate transformation that preserves the form of the elliptic equation is the modified Lorentz transformation that we have formulated in our work on Euclidean relativity and the associated space is the elliptic, or Euclidean, relativistic spacetime. As we will show in this work, equations that comply with elliptic relativity are the equations that describe the subfields of Maxwell and Dirac field. And the coordinate transformation that preserves the form of the parabolic equation is the Euclidean transformation consisting of the translation and rotation in the spatial space and the associated space is the parabolic relativistic spacetime, which is a Euclidean space with a universal time. Typical equations in physics that comply with parabolic relativity are the diffusion equation, the Schrödinger equation and in particular the diffusion equations that are derived from the four-current defined in terms of the differentiable structures of the spacetime manifold, and the Ricci flow.展开更多
Based on the analytical expression of relativistic free energy for a weakly interacting Fermi gas in a weak magnetic field, by using the method of quantum statistics, the stability conditions of the system at both hig...Based on the analytical expression of relativistic free energy for a weakly interacting Fermi gas in a weak magnetic field, by using the method of quantum statistics, the stability conditions of the system at both high and low temperatures are given, and the effects of magnetic field and interparticle interactions on the stability of the system are analysed. It is shown that at high temperatures, the stability conditions of the system are completely the same, no matter whether it is the ultrarelativistic case or nonrelativistic case. At extremely low temperatures, the mechanical stability conditions of the system show a similar rule through a comparison between the ultrarelativistic case and nonrelativistic case. At the same time, thermal stability of a relativistic Bose gas in a weak magnetic field is discussed, and the influence of the effect of relativity on the thermal stability of the system is investigated.展开更多
The Lagrangian of Einstein's special relativity with universal parameter c(SR_c)is invariant under Poincarétransformation,which preserves Lorentz metricη_μν.The SR_c has been extended to be one which is in...The Lagrangian of Einstein's special relativity with universal parameter c(SR_c)is invariant under Poincarétransformation,which preserves Lorentz metricη_μν.The SR_c has been extended to be one which is invariant underde Sitter transformation that preserves so-called Beltrami metric B_(μv).There are two universal parameters,c and R,inthis Special Relativity(denoted as SR_(cR)).The Lagrangian-Hamiltonian formulism of SR_(cR)is formulated in this paper.The canonic energy,canonic momenta,and 10 Noether charges corresponding to the space-time's,de Sitter symmetryare derived.The canonical quantization of the mechanics for SR_(CR)-free particle is performed.The physics related to itis discussed.展开更多
The aim of this review is to highlighte the common aspects between Symmetry in Physics and the Relativity Theory, particularly Special Relativity. After a brief historical introduction, emphasis is put on the physical...The aim of this review is to highlighte the common aspects between Symmetry in Physics and the Relativity Theory, particularly Special Relativity. After a brief historical introduction, emphasis is put on the physical foundations of Relativity Theory and its essential role in the clarification of many issues related to fundamental symmetries. Their different connections will be shown from Classical Mechanics to Modern Particle Physics.展开更多
Based on general relativity, J. R. Oppenheimer proved that massive celestial bodies may collapse into singular black holes with infinite densities. By analyzing the original paper of Oppenheimer, this paper reveals th...Based on general relativity, J. R. Oppenheimer proved that massive celestial bodies may collapse into singular black holes with infinite densities. By analyzing the original paper of Oppenheimer, this paper reveals that the calculations had a series and serious of mistakes. The basic problem is that the calculation supposes that the density of celestial body does not change with space-time coordinates. The density is firstly assumed invariable with space coordinates and then it is assumed invariable with time. But at last, the conclusion that the density of a celestial body becomes infinity is deduced. The premise contradicts with conclusion. In fact, there is no restriction on the initial density and radius for celestial body in the calculation. According to the calculation results of Oppenheimer, a cloud of thin gas may also collapse into singular black hole under the action of gravity. The calculations neglect great rotating speeds of massive and high density celestial bodies which would make them falling apart rather than collapsing into singularities. Because we do not know the function relations that material densities depend on space-time coordinates in advance, there exists the rationality problem of procedure using the Einstein’s equation of gravity field to calculate material collapse. Besides these physical problems, the calculation of Oppenheimer also has some obvious mistakes in mathematics. Another improved method to calculate massive celestial body’s collapse also has similar problems. The results are also unreliable. The conclusion of this paper is that up to now general relativity actually has not proved that massive celestial bodies may collapse into singularity black holes.展开更多
We verify that the total angular momentum 3-vector defined by the author [X. Zhang, Commun. Math.Phys. 206 (1999) 137] is equal to (0, 0, ma) forany time slice in both the Kerr and the Kerr-Newman spacetimes.
Previous work by Sigalotti in 2006 and recently by Hendi and Sharifzadeh in 2012 showed that all the fundamental equations of special relativity may be derived from a golden mean proportioned classical-Euclidean trian...Previous work by Sigalotti in 2006 and recently by Hendi and Sharifzadeh in 2012 showed that all the fundamental equations of special relativity may be derived from a golden mean proportioned classical-Euclidean triangle and confirmed Einstein’s famous equation E=mc2. In the present work it is shown that exchanging the Euclidean triangle with a hyperbolic one an extended quantum relativity energy equation, namely , is obtained. The relevance of this result in understanding the true nature of the “missing” so-called dark energy of the cosmos is discussed in the light of the fact that the ratio of to E=mc2 is which agrees almost completely with the latest supernova and WMAP cosmological measurements. To put it succinctly what is really missing is a quantum mechanical factor equal 1/22 in Einstein’s purely relativistic equation. This factor on the other hand is derivable from the intrinsic hyperbolic Cantor set nature of quantum entanglement.展开更多
This is a follow of previous work entitled "One Electron Atom in Special Relativity with de Sitter SpaceTime Symmetry" [Commun. Theor. Phys. 57(2012) 930]. In this paper, we consider the higher order calcula...This is a follow of previous work entitled "One Electron Atom in Special Relativity with de Sitter SpaceTime Symmetry" [Commun. Theor. Phys. 57(2012) 930]. In this paper, we consider the higher order calculations and contributions in the previous framework to solve one electron atoms in de Sitter invariant relativistic quantum mechanics. The next-to-leading-order calculations in 1/R2-expansions show that the fine-structure constant α is variant with cosmologic time going by in the de Sitter invariant special relativistic quantum mechanics with standard FRW cosmologic model.展开更多
The speed of Neutrino particles is shown to be greater than that of light as shown by the OPERA neutrino experiment at the underground Gran Sasso Laboratory. The result of this experiment can be explained within the f...The speed of Neutrino particles is shown to be greater than that of light as shown by the OPERA neutrino experiment at the underground Gran Sasso Laboratory. The result of this experiment can be explained within the framework of the Generalized Special Relativity and Savickas model.展开更多
The paper is concerned with the formulation of the static problem of general relativity. As known, this problem is reduced to ten equations for the compo-nents of the Einstein tensor and the solution of these equation...The paper is concerned with the formulation of the static problem of general relativity. As known, this problem is reduced to ten equations for the compo-nents of the Einstein tensor and the solution of these equations is associated with two principal problems. First, since the components of the Einstein tensor identically satisfy four conservation equations, only six of these equations are mutually independent. So, the set of the Einstein equations actually contains six independent equations for ten components of the metric tensor and should be supplemented with four additional equations which are missing in the original theory. Second, for a deformable solid the Einstein tensor is associated with the energy tensor which is expressed in terms of six stresses induced by gravitation. These stresses are not known and the relativity theory does not propose any equations for them. Thus, the static problem of general relativity cannot be properly formulated because the set of governing equations is not complete. In the paper, the problem of completeness of the general relativity governing set of equations is analyzed in application to the spherically symmetric static problem and the proposed approach is further described for the general case. As an example, linearized axisymmetric problem is considered.展开更多
Since the advent of relativity, it is widely accepted that the law of conservation of energy must include the energy created by disintegration of matter, or converted into matter. The aim of the present paper deals wi...Since the advent of relativity, it is widely accepted that the law of conservation of energy must include the energy created by disintegration of matter, or converted into matter. The aim of the present paper deals with the insertion of this concept into the basic equations of thermodynamics.展开更多
Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity.Though this is abeautiful idea, which may resolve many long standing problems in the theories of gravity, it also raises many otherprob...Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity.Though this is abeautiful idea, which may resolve many long standing problems in the theories of gravity, it also raises many otherproblems.In this article I will comment on some of the problems of Verlinde’s proposal with special emphasis on thethermodynamical origin of the principle of relativity.It is found that there is a large group of hidden symmetries ofthermodynamics, which contains the Poincare group of the spacetime for which space is emergent.This explains thethermodynamic origin of the principle of relativity.展开更多
In this paper Nottale’s acclaimed scale relativity theory is given a transfinite Occam’s razor leading to exact predictions of the missing dark energy [1,2] of the cosmos. It is found that 95.4915% of the energy in ...In this paper Nottale’s acclaimed scale relativity theory is given a transfinite Occam’s razor leading to exact predictions of the missing dark energy [1,2] of the cosmos. It is found that 95.4915% of the energy in the cosmos according to Einstein’s prediction must be dark energy or not there at all. This percentage is in almost complete agreement with actual measurements.展开更多
Einstein＇s field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-I universe by assuming that the cosmological term is proportional...Einstein＇s field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-I universe by assuming that the cosmological term is proportional to R-m （R is a scale factor and m is a constant）.A variety of solutions are presented.The physical significance of the respective cosmological models are also discussed.展开更多
As with the laser interferometer gravitational-wave observatory(LIGO),the matched filtering technique will be critical to the data analysis of gravitational wave detection by space-based detectors,including LISA,Taiji...As with the laser interferometer gravitational-wave observatory(LIGO),the matched filtering technique will be critical to the data analysis of gravitational wave detection by space-based detectors,including LISA,Taiji and Tianqin.Waveform templates are the basis for such matched filtering techniques.To construct ready-to-use waveform templates,numerical relativity waveforms are a starting point.Therefore,the accuracy issue of numerical relativity waveforms is critically important.There are many investigations regarding this issue with respect to LIGO.But unfortunately there are few results on this issue with respect to space-based detectors.The current paper investigates this problem.Our results indicate that the existing numerical relativity waveforms are as accurate as 99%with respect to space-based detectors,including LISA,Taiji and Tianqin.Such an accuracy level is comparable to that with respect to LIGO.展开更多
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.
基金The National Natural Science Foundation of China(No.50674086)Specialized Research Fund for the Doctoral Program of Higher Education(No.20060290508)the Science and Technology Fund of China University of Mining and Technology(No.2007B016)
文摘An association rules mining method based on semantic relativity is proposed to solve the problem that there are more candidate item sets and higher time complexity in traditional association rules mining.Semantic relativity of ontology concepts is used to describe complicated relationships of domains in the method.Candidate item sets with less semantic relativity are filtered to reduce the number of candidate item sets in association rules mining.An ontology hierarchy relationship is regarded as a directed acyclic graph rather than a hierarchy tree in the semantic relativity computation.Not only direct hierarchy relationships,but also non-direct hierarchy relationships and other typical semantic relationships are taken into account.Experimental results show that the proposed method can reduce the number of candidate item sets effectively and improve the efficiency of association rules mining.
文摘Sapir-Whorf Hypothesis is controversial, but the Linguistic Relativity is universally accepted by scholars. Through ana lyzing the causes of the mistakes that students often make during English learning and the relationship among thoughts, cultures and languages, this paper argues that language can influence people's thoughts and people's thoughts can influence the acquisi tion of a second language.
基金Supported partially by the National Natural Science Foundation of China under Grant Nos 90103004, 90403023, 10375087 and 10373003.
文摘Since the special relativity can be viewed as the physics in an inverse Wick rotation of four-dimensional （4D） Euclid space, which is at almost equal footing with the 4D Riemann/Lobachevski space, there should be important physics in the inverse Wick rotation of 4D Riemann/Lobachevski space. Thus, there are three kinds of special relativity in de Sitter（dS）/Minkowski/anti-de Sitter（AdS） space at almost equal footing, respectively. There is an instanton tunnelling scenario in the Riemann-de Sitter case that may explain why A be positive and link with the multiverse.
文摘We discuss one-dimensional Dirac oscillator, by using the concept doubly special relativity. We calculate the energy spectrum by using the concept doubly special relativity. Then, we derive another representation that the coordinate operator remains unchanged at the high energy while the momentum operator is deformed at the high energy so that it may be bounded from the above. Actually, we study the Dirac oscillator by using of the generalized uncertainty principle version and the concept doubly special relativity.
文摘In this work, we discuss the possibility to classify relativity in accordance with the classification of second order partial differential equations that have been applied into the formulation of physical laws in physics. In mathematics, since second order partial differential equations can be classified into hyperbolic, elliptic or parabolic type, therefore we show that it is also possible to classify relativity accordingly into hyperbolic, elliptic or parabolic type by establishing coordinate transformations that preserve the forms of these second order partial differential equations. The coordinate transformation that preserves the form of the hyperbolic equation is the Lorentz transformation and the associated space is the hyperbolic, or pseudo-Euclidean, relativistic spacetime. Typical equations in physics that comply with hyperbolic relativity are Maxwell and Dirac equations. The coordinate transformation that preserves the form of the elliptic equation is the modified Lorentz transformation that we have formulated in our work on Euclidean relativity and the associated space is the elliptic, or Euclidean, relativistic spacetime. As we will show in this work, equations that comply with elliptic relativity are the equations that describe the subfields of Maxwell and Dirac field. And the coordinate transformation that preserves the form of the parabolic equation is the Euclidean transformation consisting of the translation and rotation in the spatial space and the associated space is the parabolic relativistic spacetime, which is a Euclidean space with a universal time. Typical equations in physics that comply with parabolic relativity are the diffusion equation, the Schrödinger equation and in particular the diffusion equations that are derived from the four-current defined in terms of the differentiable structures of the spacetime manifold, and the Ricci flow.
文摘Based on the analytical expression of relativistic free energy for a weakly interacting Fermi gas in a weak magnetic field, by using the method of quantum statistics, the stability conditions of the system at both high and low temperatures are given, and the effects of magnetic field and interparticle interactions on the stability of the system are analysed. It is shown that at high temperatures, the stability conditions of the system are completely the same, no matter whether it is the ultrarelativistic case or nonrelativistic case. At extremely low temperatures, the mechanical stability conditions of the system show a similar rule through a comparison between the ultrarelativistic case and nonrelativistic case. At the same time, thermal stability of a relativistic Bose gas in a weak magnetic field is discussed, and the influence of the effect of relativity on the thermal stability of the system is investigated.
基金National Natural Science Foundation of China under Grant No.90403021the Doctoral Progran Funds of the Ministry of Education of China under Grant No.20020358040
文摘The Lagrangian of Einstein's special relativity with universal parameter c(SR_c)is invariant under Poincarétransformation,which preserves Lorentz metricη_μν.The SR_c has been extended to be one which is invariant underde Sitter transformation that preserves so-called Beltrami metric B_(μv).There are two universal parameters,c and R,inthis Special Relativity(denoted as SR_(cR)).The Lagrangian-Hamiltonian formulism of SR_(cR)is formulated in this paper.The canonic energy,canonic momenta,and 10 Noether charges corresponding to the space-time's,de Sitter symmetryare derived.The canonical quantization of the mechanics for SR_(CR)-free particle is performed.The physics related to itis discussed.
文摘The aim of this review is to highlighte the common aspects between Symmetry in Physics and the Relativity Theory, particularly Special Relativity. After a brief historical introduction, emphasis is put on the physical foundations of Relativity Theory and its essential role in the clarification of many issues related to fundamental symmetries. Their different connections will be shown from Classical Mechanics to Modern Particle Physics.
文摘Based on general relativity, J. R. Oppenheimer proved that massive celestial bodies may collapse into singular black holes with infinite densities. By analyzing the original paper of Oppenheimer, this paper reveals that the calculations had a series and serious of mistakes. The basic problem is that the calculation supposes that the density of celestial body does not change with space-time coordinates. The density is firstly assumed invariable with space coordinates and then it is assumed invariable with time. But at last, the conclusion that the density of a celestial body becomes infinity is deduced. The premise contradicts with conclusion. In fact, there is no restriction on the initial density and radius for celestial body in the calculation. According to the calculation results of Oppenheimer, a cloud of thin gas may also collapse into singular black hole under the action of gravity. The calculations neglect great rotating speeds of massive and high density celestial bodies which would make them falling apart rather than collapsing into singularities. Because we do not know the function relations that material densities depend on space-time coordinates in advance, there exists the rationality problem of procedure using the Einstein’s equation of gravity field to calculate material collapse. Besides these physical problems, the calculation of Oppenheimer also has some obvious mistakes in mathematics. Another improved method to calculate massive celestial body’s collapse also has similar problems. The results are also unreliable. The conclusion of this paper is that up to now general relativity actually has not proved that massive celestial bodies may collapse into singularity black holes.
文摘We verify that the total angular momentum 3-vector defined by the author [X. Zhang, Commun. Math.Phys. 206 (1999) 137] is equal to (0, 0, ma) forany time slice in both the Kerr and the Kerr-Newman spacetimes.
文摘Previous work by Sigalotti in 2006 and recently by Hendi and Sharifzadeh in 2012 showed that all the fundamental equations of special relativity may be derived from a golden mean proportioned classical-Euclidean triangle and confirmed Einstein’s famous equation E=mc2. In the present work it is shown that exchanging the Euclidean triangle with a hyperbolic one an extended quantum relativity energy equation, namely , is obtained. The relevance of this result in understanding the true nature of the “missing” so-called dark energy of the cosmos is discussed in the light of the fact that the ratio of to E=mc2 is which agrees almost completely with the latest supernova and WMAP cosmological measurements. To put it succinctly what is really missing is a quantum mechanical factor equal 1/22 in Einstein’s purely relativistic equation. This factor on the other hand is derivable from the intrinsic hyperbolic Cantor set nature of quantum entanglement.
基金Supported in part by National Natural Science Foundation of China under Grant No.11375169
文摘This is a follow of previous work entitled "One Electron Atom in Special Relativity with de Sitter SpaceTime Symmetry" [Commun. Theor. Phys. 57(2012) 930]. In this paper, we consider the higher order calculations and contributions in the previous framework to solve one electron atoms in de Sitter invariant relativistic quantum mechanics. The next-to-leading-order calculations in 1/R2-expansions show that the fine-structure constant α is variant with cosmologic time going by in the de Sitter invariant special relativistic quantum mechanics with standard FRW cosmologic model.
文摘The speed of Neutrino particles is shown to be greater than that of light as shown by the OPERA neutrino experiment at the underground Gran Sasso Laboratory. The result of this experiment can be explained within the framework of the Generalized Special Relativity and Savickas model.
文摘The paper is concerned with the formulation of the static problem of general relativity. As known, this problem is reduced to ten equations for the compo-nents of the Einstein tensor and the solution of these equations is associated with two principal problems. First, since the components of the Einstein tensor identically satisfy four conservation equations, only six of these equations are mutually independent. So, the set of the Einstein equations actually contains six independent equations for ten components of the metric tensor and should be supplemented with four additional equations which are missing in the original theory. Second, for a deformable solid the Einstein tensor is associated with the energy tensor which is expressed in terms of six stresses induced by gravitation. These stresses are not known and the relativity theory does not propose any equations for them. Thus, the static problem of general relativity cannot be properly formulated because the set of governing equations is not complete. In the paper, the problem of completeness of the general relativity governing set of equations is analyzed in application to the spherically symmetric static problem and the proposed approach is further described for the general case. As an example, linearized axisymmetric problem is considered.
文摘Since the advent of relativity, it is widely accepted that the law of conservation of energy must include the energy created by disintegration of matter, or converted into matter. The aim of the present paper deals with the insertion of this concept into the basic equations of thermodynamics.
基金Supported by the National Natural Science Foundation of China under Grant No.10875059
文摘Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity.Though this is abeautiful idea, which may resolve many long standing problems in the theories of gravity, it also raises many otherproblems.In this article I will comment on some of the problems of Verlinde’s proposal with special emphasis on thethermodynamical origin of the principle of relativity.It is found that there is a large group of hidden symmetries ofthermodynamics, which contains the Poincare group of the spacetime for which space is emergent.This explains thethermodynamic origin of the principle of relativity.
文摘In this paper Nottale’s acclaimed scale relativity theory is given a transfinite Occam’s razor leading to exact predictions of the missing dark energy [1,2] of the cosmos. It is found that 95.4915% of the energy in the cosmos according to Einstein’s prediction must be dark energy or not there at all. This percentage is in almost complete agreement with actual measurements.
文摘Einstein＇s field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-I universe by assuming that the cosmological term is proportional to R-m （R is a scale factor and m is a constant）.A variety of solutions are presented.The physical significance of the respective cosmological models are also discussed.
基金supported in part by the National Key Research and Development Program of China(Grant No.2021YFC2203001)in part by the NSFC(No.11920101003,No.12021003,No.12005016)+1 种基金supported by‘the Interdiscipline Research Funds of Beijing Normal University’CAS Project for Young Scientists in Basic Research YSBR-006。
文摘As with the laser interferometer gravitational-wave observatory(LIGO),the matched filtering technique will be critical to the data analysis of gravitational wave detection by space-based detectors,including LISA,Taiji and Tianqin.Waveform templates are the basis for such matched filtering techniques.To construct ready-to-use waveform templates,numerical relativity waveforms are a starting point.Therefore,the accuracy issue of numerical relativity waveforms is critically important.There are many investigations regarding this issue with respect to LIGO.But unfortunately there are few results on this issue with respect to space-based detectors.The current paper investigates this problem.Our results indicate that the existing numerical relativity waveforms are as accurate as 99%with respect to space-based detectors,including LISA,Taiji and Tianqin.Such an accuracy level is comparable to that with respect to LIGO.
