Abstract
We discuss numerical solutions of Einstein's field equation describing static, spherically symmetric conglomerations of a photon gas. These equations imply a back reaction of the metric on the energy density of the photon gas according to Tolman's equation. The 3–fold of solutions corresponds to a class of physically different solutions which is parameterized by only two quantities, i.e. mass and surface temperature. The energy density is typically concentrated on a shell because the center contains a repelling singularity, which can, however, not be reached by timelike geodesics and only by radial null geodesics. The physical relevance of these solutions is completely open, although their existence may raise some doubts w.r.t. the stability of black holes.
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Schmidt, H., Homann, F. Photon Stars. General Relativity and Gravitation 32, 919–931 (2000). https://doi.org/10.1023/A:1001989125318
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DOI: https://doi.org/10.1023/A:1001989125318