Generalized second law and entropy bound for a Reissner- Nordstr\"om black hole

TL;DR

This paper investigates the generalized second law of thermodynamics for Reissner-Nordström black holes, proposing modifications to the radiation's equation of state near the horizon to ensure entropy conservation and deriving an entropy-to-energy bound.

Contribution

It introduces a modified equation of state for radiation near the black hole horizon to uphold the generalized second law for charged black holes.

Findings

An upper bound on entropy-to-energy ratio similar to Bekenstein's bound is derived.

The study suggests that GSL conservation may require modifications to radiation properties near the horizon.

Abstract

It has been conjectured that black hole interacting with its surroundings will obey the Generalized Second Law ($GSL$) of thermodynamics. Conservation of $GSL$ is due to the fully thermal nature of Hawking radiation and an upper bound on entropy. We study these aspects for a Reissner-Nordstr$\ddot{\textbf{o}}$m ($RN$)black hole and conjecture that $GSL$ may be conserved if the equation of state of radiation near the horizon is modified. An upper bound on $S/E$, similar to the Bekenstein form evolves in the calculation.