Self-gravitating radiation in anti-de sitter space

Equilibrium configurations of self-gravitating massless thermal radiation inside spherical boxes of radiusR in asymptotically anti-de Sitter space (A = -3/b ₂) are constructed numerically for a range of central densities. For each box radius considered (R/b = 0, 1/2, 1, 2, 4, ), there is a unique configuration with maximal total mass and entropy, and another (at a lower central density) with maximum asymptotic red-shifted temperature. With the box removed toR=, the maximum total mass and entropy of self-gravitating thermal radiation areM _max 0.4598b0.7964(–A)^–1/2 andS _max1.3560a ^1/4 b ^3/2 3.0910a ^1/4(–A)^–3/4, and the maximum red-shifted temperature is