2001/09/30 by Rong-Gen Cai · 21 citations
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Black hole (networking) #Black hole thermodynamics #Cosmological constant #Cosmology and Gravitation Theories #Curvature #Einstein #Event horizon #Extremal black hole #Gauss–Bonnet theorem #Geometry #Horizon #Hypersurface #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Spacetime #de Sitter–Schwarzschild metric #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.65.084014
published as Phys.Rev.D65:084014,2002 · Revtex, 17 pages with 9 eps figures, v2: section II removed and references added, the version to appear in PRD
arxiv created 2002/01/12 · openalex publication_date 2002/03/25 · arxiv updated 2011/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the thermodynamic properties and phase structures of topological black holes in Einstein theory with a Gauss-Bonnet term and a negative cosmological constant. The event horizon of these topological black holes can be a hypersurface with positive, zero, or negative constant curvature. When the horizon is a zero curvature hypersurface, the thermodynamic properties of black holes are completely the same as those of black holes without the Gauss-Bonnet term, although the two black hole solutions are quite different. When the horizon is a negative constant curvature hypersurface, the thermodynamic properties of the Gauss-Bonnet black holes are qualitatively similar to those of black holes without the Gauss-Bonnet term. When the event horizon is a hypersurface with positive constant curvature, we find that the thermodynamic properties and phase structures of black holes drastically depend on the spacetime dimension d and the coefficient of the Gauss-Bonnet term: when d>~6, the properties of black holes are also qualitatively similar to the case without the Gauss-Bonnet term, but when d=5, a new phase of locally stable small blacks holes occurs under a critical value of the Gauss-Bonnet coefficient, and beyond the critical value, the black holes are always thermodynamically stable. However, the locally stable small black hole is not globally preferred; instead a thermal anti--de Sitter space is globally preferred. We find that there is a minimal horizon radius, below which the Hawking-Page phase transition will not occur since for these black holes the thermal anti--de Sitter space is always globally preferred.