One-Loop Corrected Thermodynamics of the Extremal and Non-Extremal Spinning BTZ Black Hole

TL;DR

This paper investigates the one-loop quantum corrections to the geometry and thermodynamics of rotating BTZ black holes, highlighting differences between extremal and non-extremal cases and proposing a generalized third law of thermodynamics.

Contribution

It introduces two methods for analyzing extremal black holes and demonstrates that only the approach treating extremal and non-extremal black holes as distinct entities yields consistent results.

Findings

Only the method considering extremal and non-extremal black holes as distinct yields regular solutions.

Supports a generalized third law of thermodynamics preventing continuous transition between black hole states.

Provides a detailed analysis of one-loop corrected thermodynamics of spinning BTZ black holes.

Abstract

We consider the one-loop corrected geometry and thermodynamics of a rotating BTZ black hole by way of a dimensionally reduced dilaton model. The analysis begins with a comprehensive study of the non-extremal solution after which two different methods are invoked to study the extremal case. The first approach considers the extremal limit of the non-extremal calculations, whereas the second treatment is based on the following conjecture: extremal and non-extremal black holes ae qualitatively distinct entities. We show that only the latter method yields regularity and consistency at the one-loop level. This is suggestive of a generalized third law of thermodynamics that forbids continuous evolution from non-extremal to extremal black hole geometries.