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

TL;DR

This paper explores the thermodynamics and quantum geometry of near-extreme black holes and acceleration horizons, revealing that quantum radiation entropy is solely due to the Unruh effect and analyzing quantum backreaction effects.

Contribution

It introduces a general framework for the entropy of radiation near nonextreme black holes approaching extremality and derives quantum-corrected geometries, highlighting the impact of quantum backreaction on spacetime.

Findings

Quantum radiation entropy $S_q$ is zero for acceleration horizons.

Quantum backreaction can change spacetime from AdS to dS geometry.

The first law of thermodynamics confirms $S_q=0$ for these horizons.

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 $\Lambda_{eff\text{}}$ and can drastically change the character of spacetime depending on the sign of $\Lambda _{eff}$ --- for instance, turn $AdS_{2}\times S_{2}$ into $dS_{2}\times S_{2}$ or $Rindler_{2}\times S_{2}$. Two latter solutions can be thought of as the quantum versions of the cold and ultracold limits of the Reissner-Nordstrom-de Sitter metric.