Matching radiation-dominated and matter-dominated Einstein–de Sitter universes and an application for primordial black holes in evolving cosmological backgrounds

By matching across a surface of constant time, it is demonstrated that the spacetime for a radiation-dominated Einstein–de Sitter universe can be directly matched to the spacetime for a matter-dominated Einstein–de Sitter universe. Thus, this can serve as a model of a universe filled with radiation that suddenly is converted to matter and antimatter, or a universe filled with matter and antimatter that suddenly annihilates to leave radiation. This matching is shown to hold for asymptotically Einstein–de Sitter cosmological black hole spacetimes, yielding simplistic models of primordial black holes that evolve between being in radiation-dominated universes and matter-dominated universes.     

Schwarzchild-de Sitter 黑洞的热力学性质

在考虑黑洞视界与宇宙视界具有关联性的基础上,证明de Sitter时空的热力学熵为黑洞视界热力学熵与宇宙视界热力学熵之和.给出了考虑两视界具有关联性后的de Sitter时空的热力学特性.研究表明,de Sitter时空的能量上限为纯de Sitter时空能量,deSitter时空的热容量是负的,de Sitter时空一般是量子力学不稳定的.     

Anisotropic perturbation of de Sitter space

A model-independent expression for the Friedmann equation in Bianchi type spaces is derived. In addition, a model-independent stability analysis of the higher curvature de Sitter solution is discussed. Stability conditions of the de Sitter solution are derived explicitly for a cubic model with interesting effects. It is known that quadratic terms do not contribute to this de Sitter background solution. Higher curvature terms are all critical to the stability of the de Sitter space. PACS 98.80.Cq; 04.20.-q; 04.20.Cv     

Asymptotically anti-de Sitter spaces

Asymptotically anti-de Sitter spaces are defined by boundary conditions on the gravitational field which obey the following criteria: (i) they are O(3, 2) invariant; (ii) they make the O(3, 2) surface integral charges finite; (iii) they include the Kerr-anti-de Sitter metric. An explicit expression of the O(3, 2) charges in terms of the canonical variables is given. These charges are shown to close in the Dirac brackets according to the anti-de Sitter algebra. The results are extended to the case ofN=1 supergravity. The coupling to gravity of a third-rank, completely antisymmetric, abelian gauge field is also considered. That coupling makes it possible to vary the cosmological constant and to compare the various anti-de Sitter spaces which are shown to have the same energy.On leave from Département de Physique, Université Libre de Bruxelles, BelgiumChercheur qualifié du Fonds National Belge de la Recherche Scientifique     

Thermodynamics of de Sitter Black Holes in Massive Gravity

In this paper, by taking de Sitter space-time as a thermodynamic system, we study the effective thermodynamic quantities of de Sitter black holes in massive gravity, and furthermore obtain the effective thermodynamic quantities of the space-time. Our results show that the entropy of this type of space-time takes the same form as that in Reissner-Nordstr¨om-de Sitter space-time, which lays a solid foundation for deeply understanding the universal thermodynamic characteristics of de Sitter space-time in the future. Moreover, our analysis indicates that the effective thermodynamic quantities and relevant parameters play a very important role in the investigation of the stability and evolution of de Sitter space-time.     

Unruh–DeWitt Detectors in Spherically Symmetric Dynamical Space-Times

In the present paper, Unruh–DeWitt detectors are used in order to investigate the issue of temperature associated with a spherically symmetric dynamical space-times. Firstly, we review the semi-classical tunneling method, then we introduce the Unruh–DeWitt detector approach. We show that for the generic static black hole case and the FRW de Sitter case, making use of peculiar Kodama trajectories, semiclassical and quantum field theoretic techniques give the same standard and well known thermal interpretation, with an associated temperature, corrected by appropriate Tolman factors. For a FRW space-time interpolating de Sitter space with the Einstein–de Sitter universe (that is a more realistic situation in the frame of ΛCDM cosmologies), we show that the detector response splits into a de Sitter contribution plus a fluctuating term containing no trace of Boltzmann-like factors, but rather describing the way thermal equilibrium is reached in the late time limit. As a consequence, and unlike the case of black holes, the identification of the dynamical surface gravity of a cosmological trapping horizon as an effective temperature parameter seems lost, at least for our co-moving simplified detectors. The possibility remains that a detector performing a proper motion along a Kodama trajectory may register something more, in which case the horizon surface gravity would be associated more likely to vacuum correlations than to particle creation.     

De Sitter gauge theories of gravity

The two types of de Sitter gravities are constructed with the fiber bundle technique and some special cases are discussed. Relations among de Sitter, Poincaré, and Lorentz gravity are discussed and the contraction from the de Sitter bundle to the Poincaré bundle is demonstrated. Two types of gravitational gauge field equations are obtained by using the de Sitter-Poincaré and de Sitter-Lorentz actions. The de Sitter effect occurring in the field equations is discussed.     

Parametrical embeddings of static spherically symmetric spacetimes

An analysis for a direct calculation of the embeddings in flat spacetimes of static spherically symmetric manifolds with Lorentz metric is worked out. For each manifold with non-constant curvature we arrive at a parametrical embedding which represents an infinite geometrical multiplicity of the embedded surface. The embeddings of manifolds with constant curvature are not parametrical and can be determined univocally. Examples concerning Schwarzschild, Reissner-Weyl, de Sitter and anti-de Sitter spacetimes are considered.     

Thermodynamics of the Reissner-Nordstrm-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.     

Populating the whole landscape

Every de Sitter vacuum can transition to every other de Sitter vacuum despite any obstacle, despite intervening anti-de Sitter sinks, despite not being connected by an instanton. Eternal inflation populates the whole landscape.     

Arbitrary dimensional cosmological multi-black holes

We find cosmological black hole solutions for spacetimes of arbitrary dimension (greater than three) that are asymptotically de Sitter, and we show that these solutions can be extended to give multi-black hole solutions. We investigate the motion of a charged massive test particle in a five-dimensional extreme Reissner-Nordström de Sitter background. Furthermore we obtain Killing spinors for Reissner-Nordström de Sitter spacetimes. We also find five-dimensional cosmological black hole solutions in an asymptotically anti de Sitter spacetime and we show that these solutions are supersymmetric in the sense that they admit a supercovariantly constant spinor.     

Functional representation for the isometries of de Sitter space

We examine the Schrödinger picture for a spinless field theory in two-dimensional de Sitter space and construct an ultraviolet finite functional representation for the de Sitter Lie algebra. The one-parameter family of de Sitter vacua is found to be only phase-invariant, except for one value of the parameter where the state is truly invariant.     

Cosmological term in the general theory of relativity and localization of the de Sitter and Einstein groups

The theory of a gauge gravitational field with localization of the de Sitter group is formulated. Starting from the tetradic components of the de Sitter universe, a relationship is established between the Riemannian metric and the de Sitter gauge field. It is shown that the general theory of relativity with the cosmological term is the simplest variant of the de Sitter gauge theory of gravitation, which transforms in the limit of an infinite radius of curvature of the de Sitter universe into the Poincaré-invariant GTR without the cosmological term. A theory of a gauge gravitational field with localization of Einstein's group of motions of the uniform static universe (the Einstein group R × S0 (4)) is formulated in an analogous manner.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 8, pp. 86–90, August, 1984.     

Triangular Invariants, Three-Point Functions and Particle Stability on the de Sitter Universe

We study a class of three-point functions on the de Sitter universe and on the asymptotic cone. A blending of geometrical ideas and analytic methods is used to compute some remarkable integrals, on the basis of a generalized star-triangle identity living on the cone and on the complex de Sitter manifold. We discuss an application of the general results to the study of the stability of scalar particles on the de Sitter universe.     

Gaupta-Bleuler triplet for massless spin-3/2 field in de Sitter space

Physicists have been interested in quantization of spinor and vector free fields in 4-dimensional de Sitter space-time,in ambient space notation.The Gupta-Bleuler formalism has been extensively applied to the quantization of gauge invariant theories.The field equation of the massless spin-3/2 fields is gauge invariant in de Sitter space.In this paper,we study the quantization of massless spin-3/2 gauge fields in de Sitter space-time by the Gupta-Bleuler formalism.This triplet carries an indecomposable representation of the de Sitter group.     

On the quasinormal modes of the de Sitter spacetime

Modifying a method by Horowitz and Hubeny for asymptotically anti-de Sitter black holes, we establish the classical stability of the quasinormal modes of the de Sitter spacetime. Furthermore using a straightforward method we calculate the de Sitter quasinormal frequencies of the gravitational perturbations and discuss some properties of the radial functions of these quasinormal modes.     

Mass,action, and entropy of Taub-Bolt-de Sitter spacetimes

We apply a recent proposal for defining conserved mass in asymptotically de Sitter spacetimes to the class of Taub-Bolt-de Sitter spacetimes. We compute the action, entropy, and conserved mass of these spacetimes, and find that in certain instances the mass and entropy can exceed that of pure de Sitter spacetime, in violation of recent suggestive conjectures to the contrary.     

On thermodynamics of RN-dS black hole surrounded by the quintessence

De Sitter black holes have the black hole horizon and the cosmological horizon, and the thermodynamic quantities on the two horizons all satisfy the first law of thermodynamics. The thermodynamic quantities on the two horizons are not independent but are correlated to each other. Taking de Sitter space-time as thermodynamic system, we investigated the effective thermodynamic quantities of Reissner–Nordström de Sitter black hole surrounded by the quintessence (RN-DSQ). We obtained the effective temperature and entropy of the system by considering the corrections between the black hole horizon and the cosmological horizon. We found that the entropy of the RN-DSQ is in agreement with that of Reissner–Nordström de Sitter black hole. It offers a basis for further studying of the thermodynamic properties of de Sitter space-time.