Anti–de Sitter black holes, thermal phase transition, and holography in higher curvature gravity

2002/02/28 by Y. M. Cho, Ishwaree P. Neupane · 5 citations
Mathematics · Physics and Astronomy · #Apparent horizon #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Black hole (networking) #Cosmological constant #Cosmology and Gravitation Theories #Curvature #Einstein #Event horizon #Gauss–Bonnet theorem #Geometry #Horizon #Mathematical physics #Mathematics #Phase transition #Physics #Quantum mechanics #Scalar curvature #hep-th

paper · pdf · doi:10.1103/physrevd.66.024044

published as Phys.Rev.D66:024044,2002 · 22 pages, Revtex 4, 12+1 figures, references added, section V extended. To appear in PRD

arxiv created 2002/06/17 · openalex publication_date 2002/07/31 · arxiv updated 2011/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study anti--de Sitter black holes in the Einstein-Gauss-Bonnet and the generic R² gravity theories, evaluate different thermodynamic quantities, and also examine the possibilities of Hawking-Page--type thermal phase transitions in these theories. In the Einstein theory, with a possible cosmological term, one observes a Hawking-Page phase transition only if the event horizon is a hypersurface of positive constant curvature (k=1). But, with the Gauss-Bonnet and/or the (Riemann)² interaction terms, there may occur a similar phase transition for a horizon of negative constant curvature (k=\ensuremath-1). We examine the finite coupling effects, and find that N>5 could trigger a Hawking-Page phase transition in the latter theory. For the Gauss-Bonnet black holes, one relates the entropy of the black hole to a variation of the geometric property of the horizon based on the first law and Noether charge. With a (Riemann)² term, however, we can do this only approximately, and the two results agree when r_H\ensuremath≫L, the size of the horizon is much bigger than the AdS curvature scale. We establish some relations between bulk data associated with the AdS black hole and boundary data defined on the horizon of the AdS geometry. Following a heuristic approach, we estimate the difference between Hubble entropy (S_H) and Bekenstein-Hawking entropy (S_BH) with a (Riemann)² term, which, for k=0 and k=\ensuremath-1, implies S_BH<~S_H.

Citations

• On the Holographic Principle in a Radiation Dominated Universe
• Quantum Fields in Curved Space
• Einstein equation with quantum corrections reduced to second order
• Pair production of topological anti-de Sitter black holes
• Action, Mass and Entropy of Schwarzschild-de Sitter black holes and the de Sitter/CFT Correspondence
• Order α′ (two-loop) equivalence of the string equations of motion and the σ-model Weyl invariance conditions
• Trace anomaly driven inflation
• String Inspired Brane World Cosmology
• Black holes with unusual topology
• Thermodynamics of black holes in anti-de Sitter space
• Particle creation by black holes
• An Alternative to Compactification
• Some properties of the Noether charge and a proposal for dynamical black hole entropy
• The world as a hologram
• Black Holes and Entropy
• Topological black holes in anti-de Sitter space
• Gauss-Bonnet black holes in AdS spaces
• Higher-derivative Lagrangians, nonlocality, problems, and solutions
• Temperature, energy, and heat capacity of asymptotically anti–de Sitter black holes
• The large N limit of superconformal field theories and supergravity

Cited by

• Standard constraints on the shadow radius of black holes in d-dimensional space-time: The case of regular Einstein-Gauss-Bonnet solutions
• Gauss-Bonnet black holes in AdS spaces
• Gauss-Bonnet black holes in dS spaces
• Thermodynamics of higher dimensional topological dilation black holes with a power-law Maxwell field
• Energy-dependent topological anti-de Sitter black holes in Gauss–Bonnet Born–Infeld gravity
• Spacetime structure of static solutions in Gauss-Bonnet gravity: Neutral case