Thermodynamics of Schwarzschild-(Anti-)de Sitter Black Holes with account of quantum corrections

TL;DR

This paper investigates quantum corrections to the thermodynamics and geometry of Schwarzschild-(Anti-)de Sitter black holes using anomaly-induced effective actions, revealing modifications to temperature, mass, and entropy.

Contribution

It introduces a comprehensive analysis of quantum effects on black hole thermodynamics using large N anomaly-induced actions in both 4d and 2d frameworks, including limits to Schwarzschild and de Sitter spaces.

Findings

Quantum corrections modify black hole temperature, mass, and entropy.

Results apply to both multiply horizon S(A)dS black holes and their limits.

Quantum effects also influence the entropy of an expanding universe.

Abstract

We discuss the quantum corrections to thermodynamics (and geometry) of S(A)dS BHs using large $N$ one-loop anomaly induced effective action for dilaton coupled matter (scalars and spinors). It is found the temperature, mass and entropy with account of quantum effects for multiply horizon SdS BH and SAdS BH what also gives the corresponding expressions for their limits: Schwarzschild and de Sitter spaces. In the last case one can talk about quantum correction to entropy of expanding Universe. The anomaly induced action under discussion corresponds to 4d formulation (s-wave approximation, 4d quantum matter is minimal one) as well as 2d formulation (complete effective action, 2d quantum matter is dilaton coupled one). Hence, most of results are given for the same gravitational background with interpretation as 4d quantum corrected BH or 2d quantum corrected dilatonic BH. Quantum aspects of thermodynamics of 4d 't Hooft BH model are also considered.