Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole

TL;DR

This paper derives an exact partition function for the Euclidean BTZ black hole and finds a logarithmic correction to its entropy, consistent with known results for Schwarzschild black holes, emphasizing the role of modular invariance.

Contribution

It provides an exact expression for the BTZ black hole partition function and clarifies the origin of the logarithmic entropy correction from modular invariance.

Findings

Logarithmic correction to entropy is -3/2 log(Area).

The correction aligns with Schwarzschild black hole results.

Modular invariance explains the correction in the BTZ case.

Abstract

We derive an exact expression for the partition function of the Euclidean BTZ black hole. Using this, we show that for a black hole with large horizon area, the correction to the Bekenstein-Hawking entropy is $-3/2 log(Area)$, in agreement with that for the Schwarzschild black hole obtained in the canonical gravity formalism and also in a Lorentzian computation of BTZ black hole entropy. We find that the right expression for the logarithmic correction in the context of the BTZ black hole comes from the modular invariance associated with the toral boundary of the black hole.