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We investigate the evaporation process of a Kerr-de Sitter black hole with the Unruh-Hawking-like vacuum state, which is a realistic vacuum state modelling the evaporation process of a black hole originating from gravitational collapse. We also compute the greybody factors for gravitons, photons, and conformal-coupling massless scalar particles by using the analytic solutions of the Teukolsky equation in the Kerr-de Sitter background. It turns out that the cosmological constant quenches the amplification factor and it approaches to zero towards the critical point where the Nariai and extremal limits merge together. We confirm that even near the critical point, the superradiance of gravitons is more significant than that of photons and scalar particles. Angular momentum is carried out by particles several times faster than mass energy decreases. This means that a Kerr-de Sitter black hole rapidly spins down to a nearly Schwarzschild-de Sitter black hole before it completely evaporates. We also compute the time evolution of the Bekenstein-Hawking entropy. The total entropy of the Kerr-de Sitter black hole and cosmological horizon increases with time, which is consistent with the generalized second law of thermodynamics.
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Suppose a one-dimensional isometry group acts on a space, we can consider a submergion induced by the isometry, namely we obtain an orbit space by identification of points on the orbit of the group action. We study the causal structure of the orbit space for Anti-de Sitter space (AdS) explicitely. In the case of AdS$_3$, we found a variety of black hole structure, and in the case of AdS$_5$, we found a static four-dimensional black hole, and a spacetime which has two-dimensional black hole as a submanifold.
Two important problems in studying the quantum black hole, namely the construction of the Hilbert space and the definition of the time evolution operator on such Hilbert space, are discussed using the de Sitter background field method for an observer far from the black hole. This is achieved through the ambient space formalism. Remarkably, in this approximation (distant observer), the theory preserves unitarity and analyticity, it is free from any infrared divergence, and it renders a quantum black hole entropy that turns out to be finite.
The stability of black holes and solitons in d-dimensional Anti-de Sitter space-time against scalar field condensation is discussed. The resulting solutions are hairy black holes and solitons, respectively. In particular, we will discuss static black hole solutions with hyperbolic, flat and spherical horizon topology and emphasize that two different type of instabilities exist depending on whether the scalar field is charged or uncharged, respectively. We will also discuss the influence of Gauss-Bonnet curvature terms. The results have applications within the AdS/CFT correspondence and describe e.g. holographic insulator/conductor/superconductor phase transitions.
We study the dynamics of a spherically symmetric thin shell of perfect fluid embedded in d-dimensional Anti-de Sitter space-time. In global coordinates, besides collapsing solutions, oscillating solutions are found where the shell bounces back and forth between two radii. The parameter space where these oscillating solutions exist is scanned in arbitrary number of dimensions. As expected AdS3 appears to be singled out.
Recent work indicates that the strong cosmic censorship hypothesis is violated by nearly extremal Reissner-Nordstrom-de Sitter black holes. It was argued that perturbations of such a black hole decay sufficiently rapidly that the perturbed spacetime can be extended across the Cauchy horizon as a weak solution of the equations of motion. In this paper we consider the case of Kerr-de Sitter black holes. We find that, for any non-extremal value of the black hole parameters, there are quasinormal modes which decay sufficiently slowly to ensure that strong cosmic censorship is respected. Our analysis covers both scalar field and linearized gravitational perturbations.
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