Logarithmic corrections to black hole entropy and holography

TL;DR

This paper calculates logarithmic corrections to black hole entropy within a holographic framework, linking bulk thermodynamic fluctuations to boundary conformal field theory predictions, and provides a universal entropy function matching these corrections.

Contribution

It introduces a method to compute logarithmic entropy corrections in holography, connecting bulk thermodynamic fluctuations with boundary CFT results, and proposes a universal entropy function.

Findings

Logarithmic correction coefficient matches between bulk and boundary calculations.

Explicit computation for BTZ black hole confirms the correction form.

Proposes a boundary entropy function reproducing bulk logarithmic corrections.

Abstract

We compute logarithmic corrections to the black hole entropy $S_{\rm bh}$ in a holographic set up where the cosmological constant $\Lambda$ and Newton's constant $G_D$ are taken to be thermodynamic parameters, related to variations in bulk pressure \(P\) and central charge \(c\). In the bulk, the logarithmic corrections are of the form: $\mathcal{S} = S_{\rm bh} - k \ln S_{\rm bh} + \cdots$ arising due to fluctuations in thermodynamic volume, induced by a variable $\Lambda$, in addition to energy fluctuations. We explicitly compute this coefficient $k$ for the BTZ black hole and show that the result matches with the one coming from the logarithmic corrections to the Cardy's formula. We propose an entropy function in the CFT, which exactly reproduces the logarithmic corrections to black hole entropy in arbitrary dimensions.