Classic and Quantum Motions of Scalar Particle in Beltrami-de Sitter Spacetime

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.

Continuous phase transition of the de Sitter spacetime with charged black holes and cloud of strings and quintessence

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.

Inflation in de Sitter spacetime and CMB large scale anomaly

The influence of cosmological constant-type dark energy in the early universe is investigated. This is accommodated by a new dispersion relation in de Sitter spacetime. We perform a global fit to explore the cosmological parameter space by using the CosmoMC package with the recently released Planck TT and WMAP polarization datasets. Using the results from the global fit, we compute a new CMB temperature-temperature （TT） spectrum. The obtained TT spectrum has lower power compared with that based on the ACDM model at large scales.

Positive energy theorem for(4+1)-dimensional asymptotically anti-de Sitter spacetimes

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.

Thermodynamic quantities and phase transitions of five-dimensional de Sitter hairy spacetime

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.

Three Kinds of Special Relativity via Inverse Wick Rotation

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.

Thermodynamic Interpretation of Field Equations at Horizon of BTZ Black Hole

A spacetime horizon comprising with a black hole singularity acts like a boundary of a thermal system associated with the notions of temperature and entropy. In the case of static metric of Banados-Teitelboim-Zanelli （BTZ） black hole, the field equations near the horizon boundary can be expressed as a thermal identity dE = TdS＋ Pr dA, where E = M is the mass of BTZ black hole, dA is the change in the area of the black hole horizon when the horizon is displaced infinitesimally small, Pr is the radial pressure provided by the source of Einstein equations, S = 41πa is the entropy and T =κ/2π is the Hawking temperature associated with the horizon. This approach is studied further to generalize it for non-static BTZ black hole, showing that it is also possible to interpret the field equation near horizon as a thermodynamic identity dE = TdS ＋ PrdA ＋Ω＋dJ, where Ω＋ is the angular velocity and J is the angular momentum of BTZ black hole. These results indicate that the field equations for BTZ black hole possess intrinsic thermodynamic properties near the horizon.

Thermodynamics of the Reissner-Nordstrm-de Sitter black hole

Considering the relationship between the black hole horizon and the cosmological horizon, the thermodynamic property of the charged de Sitter spacetime is discussed. The effective temperature and energy are obtained. The result shows that the upper limit of the energy in the charged de Sitter spacetime is just the energy in the pure de Sitter spacetime. The thermal capacity of the charged de Sitter spacetime is positive, thus satisfying the thermal stability condition.