Relationship between five-dimensional black holes and de Sitter spaces

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.

17 pages

References in corpus (8)

• Temperature and entropy of Schwarzschild-de Sitter space-time
• Logarithmic Corrections to Black Hole Entropy and AdS/CFT Correspondence
• Holography in a Radiation-dominated Universe with a Positive Cosmological Constant
• The AdS/CFT Correspondence and Logarithmic Corrections to Braneworld Cosmology and the Cardy-Verlinde Formula
• Logarithmic corrections to the FRW brane cosmology from 5d Schwarzschild-deSitter black hole
• Dynamic dS/CFT correspondence using the brane cosmology
• Anti-de Sitter black holes, perfect fluids, and holography
• Logarithmic corrections to the Bekenstein_Hawking entropy for five-dimensional black holes and de Sitter spaces

Cited by in corpus (6)

• Thermodynamics of Schwarzschild-de Sitter black hole: thermal stability of Nariai black hole
• de Sitter thermodynamics and the braneworld
• Phase transitions for the topological de Sitter spaces and Schwarzschild-de Sitter black hole
• Testing Holographic Principle from Logarithmic and Higher Order Corrections to Black Hole Entropy
• Logarithmic corrections to entropy for black holes with hyperbolic horizon
• Schwarzschild-De Sitter black holes in 4+1 dimensional bulk