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Register a new userBlack Hole Relics in String Gravity: Last Stages of Hawking Evaporation
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S. Alexeyev
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One of the most intriguing problem of modern physics is the question of the endpoint of black hole evaporation. Based on Einstein-dilaton-Gauss-Bonnet four dimensional string gravity model we show that black holes do not disappear and that the end of the evaporation process leaves some relic. The possibility of experimental detection of the remnant black holes is investigated. If they really exist, such objects could be a considerable part of the non baryonic dark matter in our Universe.
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Black holes in $d < 3$ spatial dimensions are studied from the perspective of the corpuscular model of gravitation, in which black holes are described as Bose-Einstein condensates of (virtual soft) gravitons. In particular, since the energy of these gravitons should increase as the black hole evaporates, eventually approaching the Planck scale, the lower dimensional cases could provide important insight into the late stages and end of Hawking evaporation. We show that the occupation number of gravitons in the condensate scales holographically in all dimensions as $N_d sim left(L_d/ell_{rm p}right)^{d-1}$, where $L_d$ is the relevant length for the system in the $(1+d)$-dimensional space-time. In particular, this analysis shows that black holes cannot contain more than a few gravitons in $d=1$. Since dimensional reduction is a common feature of many models of quantum gravity, this result can shed light on the end of the Hawking evaporation. We also consider $(1+1)$-dimensional cosmology in the context of corpuscular gravity, and show that the Friedmann equation reproduces the expected holographic scaling as in higher dimensions.
We investigate the presence of a black hole black string phase transition in Einstein Gauss Bonnet (EGB) gravity in the large dimension limit. The merger point is the static spacetime connecting the black string phase with the black hole phase. We consider several ranges of the Gauss-Bonnet parameter. We find that there is a range when the Gauss-Bonnet corrections are subordinate to the Einstein gravity terms in the large dimension limit, and yet the merger point geometry does not approach a black hole away from the neck. We cannot rule out a topology changing phase transition as argued by Kol. However as the merger point geometry does not approach the black hole geometry asymptotically it is not obvious that the transition is directly to a black hole phase. We also demonstrate that for another range of the Gauss-Bonnet parameter, the merger point geometry approaches the black hole geometry asymptotically when a certain parameter depending on the Gauss-Bonnet parameter $alpha$ and on the parameters in the Einstein-Gauss-Bonnet black hole metric is small enough.
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.
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.
An internal singularity of a string four-dimensional black hole with second order curvature corrections is discussed. A restriction to a minimal size of a neutral black hole is obtained in the frame of the model considered. Vacuum polarization of the surrounding space-time caused by this minimal-size black hole is also discussed.
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