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A critical dimension for the self-gravitating radiation

We study the structure and the stability of a self-gravitating radiation enclosed in a spherical container in a (d+1)-dimensional spacetime. It is described by the Oppenheimer-Volkoff equation with a linear equation of state. At low dimensions, the mass-energy versus central density curve presents some damped oscillations. The self-gravitating radiation becomes dynamically and thermodynamically unstable after the first mass peak. We find that the oscillations disappear above a critical dimension d_c=9.96404372... This generalizes a similar result obtained previously for isothermal spheres in Newtonian gravity where d_c=10.

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