Self-Gravitating Hawking Atmosphere of a Black Hole Fireball: Equilibrium Configurations

Solutions to the Tolman–Oppenheimer–Volkoff equation describing the thermodynamic equilibrium between a black hole and its Hawking radiation were first investigated by Zurek and Page [1] and later by ’t Hooft [2]. These models consist of a self-gravitating radiation atmosphere surrounding a negative point mass, yielding a configuration without a causal horizon. Physically, the system can be interpreted as a black hole immersed in a blue-shifted fireball, featuring a Planck-scale density ridge at the would-be horizon. In this work, we extend the analysis of Ref. [1] to explore higher-density regimes, focusing on the transition from the Zurek-Page fireball solutions to the regular, horizonless configurations typically associated with neutron stars.

[1] W. H. Zurek and D. N. Page, Phys. Rev. D 29, 628 (1984).

[2] G. ’t Hooft, Nucl. Phys. Proc. Suppl. 68, 174–184 (1998).