Black Holes in Gravity with Conformal Anomaly and Logarithmic Term in Black Hole Entropy

TL;DR

This paper derives exact black hole solutions in semi-classical gravity with Weyl anomaly, revealing a logarithmic correction to entropy that bridges classical and microscopic descriptions.

Contribution

It provides new analytic black hole solutions with conformal anomaly effects and identifies a logarithmic entropy correction relevant for quantum gravity comparisons.

Findings

Existence of asymptotically flat and de Sitter black hole solutions

Logarithmic correction to Bekenstein-Hawking entropy

Potential link between effective action non-local terms and entropy corrections

Abstract

We present a class of exact analytic and static, spherically symmetric black hole solutions in the semi-classical Einstein equations with Weyl anomaly. The solutions have two branches, one is asymptotically flat and the other asymptotically de Sitter. We study thermodynamic properties of the black hole solutions and find that there exists a logarithmic correction to the well-known Bekenstein-Hawking area entropy. The logarithmic term might come from non-local terms in the effective action of gravity theories. The appearance of the logarithmic term in the gravity side is quite important in the sense that with this term one is able to compare black hole entropy up to the subleading order, in the gravity side and in the microscopic statistical interpretation side.