Logarithmic corrections to the Bekenstein_Hawking entropy for five-dimensional black holes and de Sitter spaces

TL;DR

This paper investigates logarithmic thermal fluctuation corrections to the entropy of five-dimensional black holes and de Sitter spaces, exploring their implications for holographic dualities and thermodynamic properties.

Contribution

It derives entropy corrections for five-dimensional TAdS black holes and TdS spaces, establishing a unified approach and analyzing their impact on holographic correspondences.

Findings

Logarithmic corrections to entropy are derived for TAdS and TdS spaces.

Thermal properties of TdS are obtained from TAdS by replacing k with -k.

The corrected Cardy-Verlinde formula is consistent for both cases.

Abstract

We calculate corrections to the Bekenstein-Hawking entropy formula for the five-dimensional topological AdS (TAdS)-black holes and topological de Sitter (TdS) spaces due to thermal fluctuations. We can derive all thermal properties of the TdS spaces from those of the TAdS black holes by replacing $k$ by $-k$. Also we obtain the same correction to the Cardy-Verlinde formula for TAdS and TdS cases including the cosmological horizon of the Schwarzschild-de Sitter (SdS) black hole. Finally we discuss the AdS/CFT and dS/CFT correspondences and their dynamic correspondences.