Entropy of semiclassical 2D dilaton black holes away from the Hawking temperature

TL;DR

This paper investigates the thermodynamic properties of semiclassical 2D dilaton black holes when their temperature deviates from the Hawking value, showing how to restore finite couplings and recover Bekenstein-Hawking entropy.

Contribution

It introduces counterterms that regularize effective couplings on the horizon, enabling consistent entropy calculations away from the Hawking temperature.

Findings

Effective couplings become finite on the horizon with counterterms.

Entropy matches Bekenstein-Hawking value in nonextreme cases.

Entropy is zero for extreme black holes.

Abstract

Recently we showed that in semiclassical 2D dilaton gravity the regularity of a black hole horizon may be compatible with divergencies of Polyakov-Liouville stresses on it, the temperature deviating from its Hawking value. This makes the question about thermal properties of such solutions non-trivial. We demonstrate that, adding to gravitation-dilaton part of the action certain counterterms, which diverge on the horizon but are finite outside it, one may achieve finiteness of the effective gravitation-dilaton couplings on the horizon. This gives for the entropy S the Bekenstein - Hawking value in the nonextreme case and S=0 in the extreme one similarly to what happens to ''standard '' black holes.