Extremal Black Holes and First Law of Thermodynamics

TL;DR

This paper investigates the thermodynamics of near-extremal black holes, demonstrating universal results that connect their entropy and first law behavior with conformal field theory descriptions and near-horizon geometries.

Contribution

It provides a low temperature expansion of the first law for extremal black holes, linking entropy calculations with CFT results and horizon geometries.

Findings

Extremal black hole entropy matches the entropy function and Cardy formula.

Leading order thermodynamics is consistent with BTZ black hole first law.

Results are universal across different near-horizon geometries and microscopic models.

Abstract

We study the low temperature expansion of the first law of thermodynamics for near-extremal black holes. We show that for extremal black holes with non-vanishing entropy, the leading order contribution yields an expression for their extremal entropy in agreement with the entropy function result and the Cardy formula for the entropy of a two dimensional chiral conformal field theory (CFT). When their entropy vanishes due to the vanishing of a one-cycle on the horizon, such leading contribution is always compatible with the first law satisfied by a BTZ black hole. These results are universal and consistent both with the presence of local AdS2 and AdS3 near horizon throats for extremal black holes and with the suggested quantum microscopic descriptions (AdS2/CFT1, Kerr/CFT and EVH/CFT).