A Note on Self-gravitating Radiation in AdS Spacetime

Abstract

In this paper we investigate the equilibrium self-gravitating radiation in higher dimensional, plane symmetric anti-de Sitter space. We find that there exist essential differences from the spherically symmetric case: In each dimension ($d\ge 4$), there are maximal mass (density), maximal entropy (density) and maximal temperature configurations, they do not appear at the same central energy density; the oscillation behavior appearing in the spherically symmetric case, does not happen in this case; and the mass (density), as a function of the central energy density, increases first and reaches its maximum at a certain central energy density and then decreases monotonically in $4\le d\le 7$, while in $d\ge 8$, besides the maximum, the mass (density) of the equilibrium configuration has a minimum: the mass (density) first increases and reaches its maximum, then decreases to its minimum and then increases to its asymptotic value monotonically. The reason causing the difference is discussed.

Revtex, 13 pages with 8 eps figures, to appear in PRD; v2: typos corrected and the version in PRD

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• Information Theoretical Approach to Detecting Quantum Gravitational Corrections
• Critical Dimension for Stable Self-gravitating Stars in AdS
• Metallic transports from Taub-NUT AdS black holes