Nonextreme black holes near the extreme state and acceleration horizons: thermodynamics and quantum-corrected geometry

Abstract

We consider the class of metrics that can be obtained from those of nonextreme black holes by limiting transitions to the extreme state such that the near-horizon geometry expands into a whole manifold. These metrics include, in particular, the Rindler and Bertotti - Robinson spacetimes. The general formula for the entropy of massless radiation valid either for black-hole or for acceleration horizons is derived. It is argued that, as a black hole horizon in the limit under consideration turns into an acceleration one, the thermodynamic entropy $S_q$ of quantum radiation is due to the Unruh effect entirely and $S_q=0$ exactly. The contribution to the quasilocal energy from a given curved spacetime is equal to zero and the only nonvanishing term stems from a reference metric. In the variation procedure necessary for the derivation of the general first law, the metric on a horizon surface changes along with the boundary one, and the account for gravitational and matter stresses is an essential ingredient of the first law. This law confirms the property $S_q=0$. The quantum-corrected geometry of the Bertotti - Robinson spacetime is found and it is argued that backreaction of quantum fields mimics the effect of the cosmological constant ${\Lambda }_{eff}$ and can drastically change the character of spacetime depending on the sign of ${\Lambda }_{eff}$ --- for instance, turn $Ad{S}_2\times S_2$ into $d{S}_2\times S_2$ or $Rindle{r}_2\times S_2$. Two latter solutions can be thought of as the quantum versions of the cold and ultracold limits of the Reissner-Nordstrom-de Sitter metric.

27 pages, REVTeX 3.0. Expanded from previous version. Title somewhat changed. Qualitative explanation of effects of strong quantum backreaction on geometry suggested in terms of induced cosmological constant. Stressed that if this constant is positive, solutions found can be considered as quantum versions of charged Nariai one. Accepted for publication in Class. Quant. Grav

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• Mapping Hawking into Unruh Thermal Properties
• Hawking radiation without black hole entropy
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• Geometry of nonextreme black holes near the extreme state
• Horizon/Matter Systems near the Extreme State
• Two kinds of extreme black holes and their classification
• Dilaton black holes in grand canonical ensemble near the extreme state
• Planckian $Ad{S}_2\times S_2$ space is an exact solution of the semiclassical Einstein equations
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• Extremal limit of the regular charged black holes in nonlinear electrodynamics
• Classical model of elementary particle with Bertotti-Robinson core and extremal black holes
• Extremal limit for charged and rotating 2+1-dimensional black holes and Bertotti-Robinson geometry
• Regular black holes in an asymptotically de Sitter universe
• Curvature tensors on distorted Killing horizons and their algebraic classification
• Quantum backreaction of massive fields and self-consistent semiclassical extreme black holes and acceleration horizons
• Semiclassical ultraextremal horizons
• Entropy of massive fields near a black hole and vacuum polarization: thermodynamics without statistical mechanics