2003/02/28 by Ishwaree P. Neupane · 110 citations
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Black hole (networking) #Bounded function #Classical mechanics #Cosmology and Gravitation Theories #Curvature #Entropy (arrow of time) #Event horizon #Geometry #Gravitation #Hyperbolic space #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Scalar curvature #Spacetime #hep-th
paper · pdf · doi:10.1103/physrevd.69.084011
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 69(8) (American Physical Society) · Shortened to match published (PRD) version, 18 pages, several eps figures
arxiv created 2004/01/12 · openalex publication_date 2004/04/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the properties of anti--de Sitter black holes with a Gauss-Bonnet term for various horizon topologies (k=0,\ifmmode±\else\textpm\fi1) and for various dimensions, with emphasis on the less well understood k=\ensuremath-1 solution. We find that the zero temperature (and zero energy density) extremal states are the local minima of the energy for AdS black holes with hyperbolic event horizons. The hyperbolic AdS black hole may be stable thermodynamically if the background is defined by an extremal solution and the extremal entropy is non-negative. We also investigate the gravitational stability of AdS spacetimes of dimensions D>4 against linear perturbations and find that the extremal states are still the local minima of the energy. For a spherically symmetric AdS black hole solution, the gravitational potential is positive and bounded, with or without the Gauss-Bonnet type corrections, while, when k=\ensuremath-1, a small Gauss-Bonnet coupling, namely, \ensuremathα\ensuremath≪l2 (where l is the curvature radius of AdS space), is found useful to keep the potential bounded from below, as required for stability of the extremal background.