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Register a new userUnitarity and the information problem in an explicit model of black hole evaporation
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We consider the black hole information problem in an explicitly defined spacetime modelling black hole evaporation. Using this context we review basic aspects of the problem, with a particular effort to be unambiguous about subtle topics, for instance precisely what is meant by entropy in various circumstances. We then focus on questions of unitarity, and argue that commonly invoked semiclassical statements of long term, evaporation time, and Page time unitarity may all be violated even if physics is fundamentally unitary. This suggests that there is no horizon firewall. We discuss how the picture is modified for regular (nonsingular) evaporation models. We also compare our conclusions to recent holographic studies, and argue that they are mutually compatible.
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An approach to black hole quantization is proposed wherein it is assumed that quantum coherence is preserved. A consequence of this is that the Penrose diagram describing gravitational collapse will show the same topological structure as flat Minkowski space. After giving our motivations for such a quantization procedure we formulate the background field approximation, in which particles are divided into hard particles and soft particles. The background space-time metric depends both on the in-states and on the out-states. We present some model calculations and extensive discussions. In particular, we show, in the context of a toy model, that the $S$-matrix describing soft particles in the hard particle background of a collapsing star is unitary, nevertheless, the spectrum of particles is shown to be approximately thermal. We also conclude that there is an important topological constraint on functional integrals.
We analyze how a quantum-gravity-induced change in the number of thermal dimensions (through a modified dispersion relation) affects the geometry and the thermodynamics of a charged black hole. To that end we resort to Kiselevs solution as the impact such modifications have on the evaporation rate of the black hole becomes more clear. As an application, we study the case for which the thermal dimension is reduced to two.
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.
We present, in an explicit form, the metric for all spherically symmetric Schwarzschild-Bach black holes in Einstein-Weyl theory. In addition to the black hole mass, this complete family of spacetimes involves a parameter that encodes the value of the Bach tensor on the horizon. When this additional non-Schwarzschild parameter is set to zero the Bach tensor vanishes everywhere and the Schwa-Bach solution reduces to the standard Schwarzschild metric of general relativity. Compared with previous studies, which were mainly based on numerical integration of a complicated form of field equations, the new form of the metric enables us to easily investigate geometrical and physical properties of these black holes, such as specific tidal effects on test particles, caused by the presence of the Bach tensor, as well as fundamental thermodynamical quantities.
We discuss the near singularity region of the linear mass Vaidya metric for massless particles with non-zero angular momentum. In particular we look at massless geodesics with non-zero angular momentum near the vanishing point of a special subclass of linear mass Vaidya metrics. We also investigate this same structure in the numerical solutions for the scattering of massless scalars from the singularity. Finally we make some comments on the possibility of using this metric as a semi-classical model for the end-point of black hole evaporation.
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