Entropy of singularities in self-gravitating radiation

The Bekenstein-Hawking entropy suggests that thermodynamics is an intrinsic ingredient of gravity. Here, we explore the idea that requirements of thermodynamic consistency could determine the gravitational entropy in other setups. We implement this idea in a simple model: static, spherically symmetric solutions to Einstein's equations corresponding to self-gravitating radiation. We find that the principle of maximum entropy provides a consistent thermodynamic description of the system, only if the entropy includes a contribution from the spacetime singularities that appear in the solutions of Einstein's equations. The form of the singularity entropy is stringently constrained from consistency requirements, so that the existence of a simple expression satisfying these constraints is highly non-trivial, and suggests a fundamental origin. We find that the system is characterized by three equilibrium phases, and we conduct a preliminary investigation of the associated phase transitions. These results demonstrate the point that gravitational entities other than horizons are endowed with thermodynamic properties. (paper)