A Note on Self-gravitating Radiation in AdS Spacetime

TL;DR

This paper explores the properties of self-gravitating radiation in higher-dimensional anti-de Sitter space, revealing unique behaviors in mass, entropy, and temperature configurations that differ from spherically symmetric cases.

Contribution

It provides a detailed analysis of equilibrium configurations of self-gravitating radiation in higher-dimensional AdS space, highlighting differences from spherical symmetry and identifying new mass-density behaviors.

Findings

Existence of maximal mass, entropy, and temperature configurations in each dimension.

Mass as a function of central energy density exhibits non-monotonic behavior in dimensions 4 to 7.

In dimensions 8 and above, mass shows a maximum, minimum, then increases monotonically.

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 ($d\geq 4$), 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 $d \geq 8$, 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.