Entropy of Higher Dimensional Charged Gauss-Bonnet Black hole in de Sitter Space

TL;DR

This paper derives the entropy formula for higher dimensional charged Gauss-Bonnet black holes in de Sitter space, revealing additional entropy terms beyond the sum of horizon entropies, which depend on horizon radius ratios.

Contribution

It introduces effective thermodynamic quantities and derives a corrected entropy formula accounting for horizon interactions in de Sitter space.

Findings

Total entropy includes extra terms beyond horizon sum.

Extra entropy terms depend on horizon radius ratio.

Corrected entropy is independent of spacetime charge.

Abstract

The fundamental equation of the thermodynamic system gives the relation between internal energy, entropy and volume of two adjacent equilibrium states. Taking higher dimensional charged Gauss-Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, the effective temperature of spacetime is the same, we conjecture that the effective temperature has the same value. In this way, we can obtain the entropy formula of spacetime by solving the differential equation. We find that the total entropy contain an extra terms besides the sum of the entropies of the two horizons. The corrected terms of the entropy is a function of horizon radius ratio, and is independent of the charge of the spacetime.