Abstract
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≈ 0.4598b≈0.7964(−A)−1/2 andS max≈1.3560a 1/4 b 3/2≈ 3.0910a 1/4(−A)−3/4, and the maximum red-shifted temperature is
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Page, D.N., Phillips, K.C. Self-gravitating radiation in anti-de sitter space. Gen Relat Gravit 17, 1029–1042 (1985). https://doi.org/10.1007/BF00774206
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DOI: https://doi.org/10.1007/BF00774206