Kerr-de Sitter Spacetime Research Articles

The First Law of Thermodynamics of the (2+1)-DimensionalBanados–Teitelboim–Zanelli Black Holes and Kerr–de Sitter Spacetimes

We investigate the first law of thermodynamics in the case of the(2+1)-dimensional Banados–Teitelboim–Zanelli black holes and Kerr–deSitter spacetimes. In particular, we focus on the integral massformulas. It is found that by assuming the cosmological constant as avariable state parameter, both the differential and integral massformulas of the first law of black hole thermodynamics in the asymptoticflat spacetimes can be directly extended to those of rotating blackholes in anti-de Sitter and de Sitter backgrounds. It should be pointedthat these formulae come into existence in any dimensions.

Erratum: Entropy of a Kerr-de Sitter black hole due to arbitrary spin fields [Phys. Rev. D69, 044019 (2004)

The Newman-Penrose formalism is used to derive the Teukolsky master equations controlling massless scalar, neutrino, electromagnetic, gravitino, and gravitational field perturbations of the Kerr-de Sitter spacetime. Then the quantum entropy of a non-extreme Kerr-de Sitter black hole due to arbitrary spin fields is calculated by the improved thin-layer brick wall model. It is shown that the subleading order contribution to the entropy is dependent on the square of the spins of particles and that of the specific angular momentum of black holes as well as the cosmological constant. The logarithmic correction of the spins of particles to the entropy relies on the rotation of the black hole and the effect of the cosmological constant.

Entropy and mass bounds of Kerr–de Sitter spacetimes

We consider Kerr-de Sitter spacetimes and evaluate their mass, angular momentum and entropy according to the boundary counterterm prescription. We provide a physicall interpretation for angular velocity and angular momentum at future/past infinity. We show that the entropy of the four-dimensional Kerr-de Sitter spacetimes is less than of pure de Sitter spacetime in agreement to the entropic N-bound. Moreover, we show that maximal mass conjecture which states any asymptotically de Sitter spacetime with mass greater than de Sitter has a cosmological singularity is respected by asymptotically de Sitter spacetimes with rotation. We furthermore consider the possibility of strengthening the conjecture to state that any asymptotically dS spacetime will have mass greater than dS if and only if it has a cosmological singularity and find that Kerr-de Sitter spacetimes do not respect this stronger statement. We investigate the behavior of the c-function for the Kerr-de Sitter spacetimes and show that it is no longer isotropic. However an average of the c-function over the angular variables yields a renormalization group flow in agreement with the expansion of spacetime at future infinity.

Separability of the Hamilton–Jacobi and Klein–Gordon equations in Kerr–de Sitter metrics

We study separability of the Hamilton–Jacobi and massive Klein–Gordon equations in the general Kerr–de Sitter spacetime in higher dimensions. Complete separation of both equations is carried out in 2n + 1 spacetime dimensions with all n rotation parameters equal, in which case the rotational symmetry group is enlarged from (U(1))n to U(n). We explicitly construct the additional Killing vectors associated with the enlarged symmetry group which permit separation. We also derive first-order equations of motion for particles in these backgrounds and examine some of their properties.

Comments on quantum aspects of three-dimensional de Sitter gravity

We investigate the quantum aspects of three-dimensional gravity with a positive cosmological constant. The reduced phase space of the three-dimensional de Sitter gravity is obtained as the space which consists of the Kerr–de Sitter spacetimes and their Virasoro deformations. A quantization of the phase space is carried out by the geometric quantization of the coadjoint orbits of the asymptotic Virasoro symmetries. The Virasoro algebras with real central charges are obtained as the quantum asymptotic symmetries. The states of globally de Sitter and point particle solutions become the primary states of the unitary irreducible representations of the Virasoro algebras. It is shown that those states are perturbatively stable at the quantum level. The Virasoro deformations of these solutions correspond to the excited states in the unitary irreducible representations. In view of the dS/CFT correspondence, we also study the relationship between the Liouville field theory obtained by a reduction of the SL(2; C) Chern–Simons theory and the three-dimensional gravity both classically and quantum mechanically. In the analyses of the both theories, the Kerr–de Sitter geometries with non-zero angular momenta do not give the unitary representations of the Virasoro algebras.

CFT description of three-dimensional Kerr–de Sitter spacetime

We describe three-dimensional Kerr–de Sitter space using similar methods as recently applied to the BTZ black hole. A rigorous form of the classical connection between gravity in three dimensions and two-dimensional conformal field theory is employed, where the fundamental degrees of freedom are described in terms of two dependent SL(2, C) currents. In contrast to the BTZ case, however, quantization does not give the Bekenstein–Hawking entropy connected to the cosmological horizon of Kerr–de Sitter space.

Kerr–de Sitter spacetimes in various dimensions and dS/CFT correspondence

We consider the Kerr-de Sitter (Kerr-dS) black hole in various dimensions. Introducing a counterterm, we show that the total action of these spacetimes are finite. We compute the masses and the angular momenta of Kerr-dS spaces with one rotational parameter in four, five and seven dimensions. These conserved charges are also computed for the case of Kerr-dS space with two rotational parameters in five dimensions. Although the angular momentum density due to the counterterm is nonzero, it gives a vanishing contribution to the total angular momentum. We also find that the total angular momentum of the spacetime is independent of the radius of the boundary for all cases, a fact that is not true for the total mass of the system.

Null geodesics in black hole metrics with non-zero cosmological constant

We study the radial motion along null geodesics in the Reissner-Nordstrom-de Sitter and Kerr-de Sitter space-times. We analyze the properties of the effective potential and we discuss circular orbits. We find that: 1) the radius of circular photon orbits in the Reissner-Nordstrom-de Sitter space-times does not depend on the cosmological constant. We show also how this is related to properties of the optical reference geometry. 2) For a specific range of the cosmological constant, photons with high impact parameter may travel radially between the cosmological horizon and the black hole horizon in the equatorial plane of the Kerr-de Sitter space-times.

Newtonian analogue of force and motion of a free particle in the gravitational field of Kerr-de Sitter space-time

In the first part of the paper the Newtonian analogue of force for the Kerr-de Sitter metric has been investigated. To the first-order of approximation, a component of the force vector corresponds to the Newtonian gravitational force and a cosmic force arising due to the cosmological constant A. Int the higher order of approximation, the relativistic correction terms due to rotation and the presence of A are obtained. In the second part of the paper the motion of a freely-falling body has been investigated. It is found that plane orbits are not possible. Also a radial fall is not possible and there is a rotational drag on the particle which has no Newtonian analogue.