Relationship between five-dimensional black holes and de Sitter spaces

TL;DR

This paper explores the deep connections between five-dimensional topological anti-de Sitter black holes and de Sitter spaces, revealing how their thermal properties and holographic correspondences are related through simple parameter substitutions.

Contribution

It demonstrates that thermal and holographic properties of TdS spaces can be derived from TAdS black holes via parameter replacements, extending the AdS/CFT correspondence to de Sitter spaces.

Findings

Thermal properties of TdS spaces relate to TAdS black holes by replacing k with -k.

Cosmological horizon properties of SdS black holes derive from hyperbolic-AdS black holes by substituting m with -m.

Logarithmic corrections to entropy and Friedmann equations are computed due to thermal fluctuations.

Abstract

We study a close relationship between the topological anti-de Sitter (TAdS)-black holes and topological de Sitter (TdS) spaces including the Schwarzschild-de Sitter (SdS) black hole in five-dimensions. We show that all thermal properties of the TdS spaces can be found from those of the TAdS black holes by replacing $k$ by $-k$. Also we find that all thermal information for the cosmological horizon of the SdS black hole is obtained from either the hyperbolic-AdS black hole or the Schwarzschild-TdS space by substituting $m$ with $-m$. For this purpose we calculate thermal quantities of bulk, (Euclidean) conformal field theory (ECFT) and moving domain wall by using the A(dS)/(E)CFT correspondences. Further we compute logarithmic corrections to the Bekenstein-Hawking entropy, Cardy-Verlinde formula and Friedmann equation due to thermal fluctuations. It implies that the cosmological horizon of the TdS spaces is nothing but the event horizon of the TAdS black holes and the dS/ECFT correspondence is valid for the TdS spaces in conjunction with the AdS/CFT correspondence for the TAdS black holes.