Entropy of Reissner-Nordstr\"om-de Sitter black hole

TL;DR

This paper proposes a new total entropy formula for Reissner-Nordström-de Sitter black holes that includes an entanglement term between the horizons, diverging as they approach each other.

Contribution

It introduces a conjecture that the total entropy includes an entanglement contribution beyond the sum of individual horizon entropies, derived using effective thermodynamics.

Findings

Total entropy diverges when horizons coincide.

Effective first law used to derive entropy.

Entanglement term modifies traditional entropy calculation.

Abstract

Based on the consideration that the black hole horizon and the cosmological horizon of Reissner-Nordstr\"om black hole in de Sitter space are not independent each other, we conjecture the total entropy of the system should have an extra term contributed from the entanglement between the two horizons, except for the sum of the two horizon entropies. Making use of the globally effective first law and the effective thermodynamic quantities, we derive the total entropy and find that it will diverge as the two horizons tends to coincide.