Logarithmic Corrections to the Black Hole Entropy Product of ${\cal H}^{\pm}$ via Cardy Formula

TL;DR

This paper calculates logarithmic corrections to the entropy product of black hole horizons using the Cardy formula, focusing on BTZ black holes, and discusses their implications for universality and quantization.

Contribution

It introduces a method to compute logarithmic entropy corrections for black hole horizons using the Cardy formula, applied specifically to BTZ black holes.

Findings

Logarithmic corrections depend on black hole parameters.

The corrected entropy product is neither universal nor quantized.

Application to BTZ black holes demonstrates the method's effectiveness.

Abstract

We compute the logarithmic corrections to black hole (BH) entropy product of ${\cal H}^{\pm}$ \footnote{ ${\cal H}^{+}$ and ${\cal H}^{-}$ denote outer (event) horizon and inner (Cauchy) horizons} by using \emph{Cardy prescription}. We particularly apply this formula for \emph{BTZ BH}. We speculate that the logarithmic corrections to entropy product of ${\cal H}^{\pm}$ when computed \emph{via Cardy formula} the product should be neither \emph{mass-independent (universal)} nor be \emph{quantized}.