From a five-dimensional Minkowski view the five-dimensional angular momentum of a free spin-O particle moving in de Sifter spacefime is conservative, by which its fimelike geodesics can be labeled completely and uniqu...From a five-dimensional Minkowski view the five-dimensional angular momentum of a free spin-O particle moving in de Sifter spacefime is conservative, by which its fimelike geodesics can be labeled completely and uniquely. Based on that observation and working in Belframi coordinate for de Sifter spacefime, solutions and their asymptotic behavior to the Belframi-de Sifter-Klein-Gordon equation are given.展开更多
Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 k...Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 killing vector fields corresponding to Witten’s five Branes model in eleven dimensional M-theory we reason that 504 of the 528 are essentially the components of the relevant killing-Yano tensor. In turn this tensor is related to hidden symmetries and torsional coupled stresses of the Cosserat micro-polar space as well as the Einstein-Cartan connection. Proceeding in this way the dark energy density is found to be that of Einstein’s maximal energy mc2 where m is the mass and c is the speed of light multiplied with a Lorentz factor equal to the ratio of the 504 killing-Yano tensor and the 528 states maximally symmetric space. Thus we have E (dark) = mc2 (504/528) = mc2 (21/22) which is about 95.5% of the total maximal energy density in astounding agreement with COBE, WMAP and Planck cosmological measurements as well as the type 1a supernova analysis. Finally theory and results are validated via a related theory based on the degrees of freedom of pure gravity, the theory of nonlocal elasticity as well as ‘t Hooft-Veltman renormalization method.展开更多
We define the total energy-momenta for(4+1)-dimensional asymptotically anti-de Sitter spacetimes,which comes from the boundary terms at infinity in the integral form of the Weitzenbck formula.Then we prove the positiv...We define the total energy-momenta for(4+1)-dimensional asymptotically anti-de Sitter spacetimes,which comes from the boundary terms at infinity in the integral form of the Weitzenbck formula.Then we prove the positive energy theorem for such spacetimes,following Witten’s original argumentsfor the positive energy theorem in asymptotically flat spacetimes.展开更多
Recently,some meaningful results have been obtained by studying the phase transition,critical exponents,and other thermodynamical properties of different black holes.Especially for the Anti-de Sitter(AdS)black holes,t...Recently,some meaningful results have been obtained by studying the phase transition,critical exponents,and other thermodynamical properties of different black holes.Especially for the Anti-de Sitter(AdS)black holes,their thermodynamical properties nearby the critical point have attracted considerable attention.However,there exists little work on the thermodynamic properties of the de Sitter(dS)spacetime with black holes.In this paper,based on the effective thermodynamical quantities and the method of the Maxwell's equal-area law,we explore the phase equilibrium for the de Sitter spacetime with the charged black holes and the cloud of string and quintessence(i.e.,C-dSSQ spacetime).The boundaries of the two-phase coexistence region in both P_(eff)−T_(eff)and T_(eff)−S diagrams are obtained.The coexistent curve and the latent heat of phase transition for this system are also investigated.Furthermore,we analyze the effect of parameters(the state parameterωand the ratio of two horizon radii x=r+/r_(c))on the two-phase coexistence region boundary.The results indicate that the phase transition in C-dSSQ spacetime is analogous to that in a van der Waals fluid(vdw)system,which is determined by the electrical potential at the horizon.These results are helpful for understanding the basic properties of black holes and are also of great value for the establishment of quantum gravity.展开更多
In this study,we take the mass,electric charge,hair parameter,and cosmological constant of five-dimensional de Sitter hairy spacetime as the state parameters of the thermodynamic system,and when these state parameters...In this study,we take the mass,electric charge,hair parameter,and cosmological constant of five-dimensional de Sitter hairy spacetime as the state parameters of the thermodynamic system,and when these state parameters satisfy the first law of thermodynamics,the equivalent thermodynamic quantities of spacetime and the Smarr relation of five-dimensional de Sitter hairy spacetime are obtained.Then,we study the thermodynamic characteristics of the spacetime described by these equivalent thermodynamic quantities and find that de Sitter hairy spacetime has a phase transition and critical phenomena similar to those of van de Waals systems or charged AdS black holes.It is shown that the phase transition point of de Sitter hairy spacetime is determined by the ratio of two event horizon positions and the cosmic event horizon position.We discuss the influence of the hair parameter and electric charge on the critical point.We also find that the isochoric heat capacity of the spacetime is not zero,which is consistent with the ordinary thermodynamic system but differs from the isochoric heat capacity of AdS black holes,which is zero.Using the Ehrenfest equations,we prove that the critical phase transition is a second order equilibrium phase transition.Research on the thermodynamic properties of five-dimensional de Sitter hairy spacetime lays a foundation for finding a universal de Sitter spacetime thermodynamic system and studying its thermodynamic properties.Our universe is an asymptotically dS spacetime,and the thermodynamic characteristics of de Sitter hairy spacetime will help us understand the evolution of spacetime and provide a theoretical basis to explore the physical mechanism of the accelerated expansion of the universe.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No.10547002
文摘From a five-dimensional Minkowski view the five-dimensional angular momentum of a free spin-O particle moving in de Sifter spacefime is conservative, by which its fimelike geodesics can be labeled completely and uniquely. Based on that observation and working in Belframi coordinate for de Sifter spacefime, solutions and their asymptotic behavior to the Belframi-de Sifter-Klein-Gordon equation are given.
文摘Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 killing vector fields corresponding to Witten’s five Branes model in eleven dimensional M-theory we reason that 504 of the 528 are essentially the components of the relevant killing-Yano tensor. In turn this tensor is related to hidden symmetries and torsional coupled stresses of the Cosserat micro-polar space as well as the Einstein-Cartan connection. Proceeding in this way the dark energy density is found to be that of Einstein’s maximal energy mc2 where m is the mass and c is the speed of light multiplied with a Lorentz factor equal to the ratio of the 504 killing-Yano tensor and the 528 states maximally symmetric space. Thus we have E (dark) = mc2 (504/528) = mc2 (21/22) which is about 95.5% of the total maximal energy density in astounding agreement with COBE, WMAP and Planck cosmological measurements as well as the type 1a supernova analysis. Finally theory and results are validated via a related theory based on the degrees of freedom of pure gravity, the theory of nonlocal elasticity as well as ‘t Hooft-Veltman renormalization method.
基金supported by National Natural Science Foundation of China(Grant No.11171328)Fundamental Research Funds for the Central Universities of China(Grant No.210274087)
文摘We define the total energy-momenta for(4+1)-dimensional asymptotically anti-de Sitter spacetimes,which comes from the boundary terms at infinity in the integral form of the Weitzenbck formula.Then we prove the positive energy theorem for such spacetimes,following Witten’s original argumentsfor the positive energy theorem in asymptotically flat spacetimes.
基金Supported by the Natural Science Foundation of China(11705106,12075143)the Scientific Innovation Foundation of the Higher Education Institutions of Shanxi Province(2020L0471,2020L0472)+2 种基金the Science Technology Plan Project of Datong City,China(2020153)the Science Foundation of Shanxi Datong University(2022Q1,2015Q6,2022Q2)the Teaching Reform Project of Shanxi Datong University(XJG2022234)。
文摘Recently,some meaningful results have been obtained by studying the phase transition,critical exponents,and other thermodynamical properties of different black holes.Especially for the Anti-de Sitter(AdS)black holes,their thermodynamical properties nearby the critical point have attracted considerable attention.However,there exists little work on the thermodynamic properties of the de Sitter(dS)spacetime with black holes.In this paper,based on the effective thermodynamical quantities and the method of the Maxwell's equal-area law,we explore the phase equilibrium for the de Sitter spacetime with the charged black holes and the cloud of string and quintessence(i.e.,C-dSSQ spacetime).The boundaries of the two-phase coexistence region in both P_(eff)−T_(eff)and T_(eff)−S diagrams are obtained.The coexistent curve and the latent heat of phase transition for this system are also investigated.Furthermore,we analyze the effect of parameters(the state parameterωand the ratio of two horizon radii x=r+/r_(c))on the two-phase coexistence region boundary.The results indicate that the phase transition in C-dSSQ spacetime is analogous to that in a van der Waals fluid(vdw)system,which is determined by the electrical potential at the horizon.These results are helpful for understanding the basic properties of black holes and are also of great value for the establishment of quantum gravity.
基金the National Natural Science Foundation of China(12075143)。
文摘In this study,we take the mass,electric charge,hair parameter,and cosmological constant of five-dimensional de Sitter hairy spacetime as the state parameters of the thermodynamic system,and when these state parameters satisfy the first law of thermodynamics,the equivalent thermodynamic quantities of spacetime and the Smarr relation of five-dimensional de Sitter hairy spacetime are obtained.Then,we study the thermodynamic characteristics of the spacetime described by these equivalent thermodynamic quantities and find that de Sitter hairy spacetime has a phase transition and critical phenomena similar to those of van de Waals systems or charged AdS black holes.It is shown that the phase transition point of de Sitter hairy spacetime is determined by the ratio of two event horizon positions and the cosmic event horizon position.We discuss the influence of the hair parameter and electric charge on the critical point.We also find that the isochoric heat capacity of the spacetime is not zero,which is consistent with the ordinary thermodynamic system but differs from the isochoric heat capacity of AdS black holes,which is zero.Using the Ehrenfest equations,we prove that the critical phase transition is a second order equilibrium phase transition.Research on the thermodynamic properties of five-dimensional de Sitter hairy spacetime lays a foundation for finding a universal de Sitter spacetime thermodynamic system and studying its thermodynamic properties.Our universe is an asymptotically dS spacetime,and the thermodynamic characteristics of de Sitter hairy spacetime will help us understand the evolution of spacetime and provide a theoretical basis to explore the physical mechanism of the accelerated expansion of the universe.
