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      Born-Infeld Black Holes in (A)dS Spaces

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          Abstract

          We study some exact solutions in a \(D(\ge4)\)-dimensional Einstein-Born-Infeld theory with a cosmological constant. These solutions are asymptotically de Sitter or anti-de Sitter, depending on the sign of the cosmological constant. Black hole horizon and cosmological horizon in these spacetimes can be a positive, zero or negative constant curvature hypersurface. We discuss the thermodynamics associated with black hole horizon and cosmological horizon. In particular we find that for the Born-Infeld black holes with Ricci flat or hyperbolic horizon in AdS space, they are always thermodynamically stable, and that for the case with a positive constant curvature, there is a critical value for the Born-Infeld parameter, above which the black hole is also always thermodynamically stable, and below which a unstable black hole phase appears. In addition, we show that although the Born-Infeld electrodynamics is non-linear, both black hole horizon entropy and cosmological horizon entropy can be expressed in terms of the Cardy-Verlinde formula. We also find a factorized solution in the Einstein-Born-Infeld theory, which is a direct product of two constant curvature spaces: one is a two-dimensional de Sitter or anti-de Sitter space, the other is a (\(D-2\))-dimensional positive, zero or negative constant curvature space.

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          Author and article information

          Journal
          13 October 2004
          2004-12-07
          Article
          10.1103/PhysRevD.70.124034
          hep-th/0410158
          cb75fe53-c2f1-442e-905d-4f419041f524
          History
          Custom metadata
          Phys.Rev.D70:124034,2004
          Latex, 18 pages with 4 eps figures, v2: Revtex, 11 pages with 4 eps figures, to appear in PRD
          hep-th gr-qc

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