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Black-hole thermodynamics and singular solutions of the Tolman-Oppenheimer-Volkoff equation
Physical Review D, Particles and fields
We investigate thermodynamic equilibrium of a self-gravitating perfect fluid in a spherically symmetric system containing a black hole of mass M by means of the Tolman-Oppenheimer-Volkoff (TOV) equation. At r >> 2M its solutions describe a black-body radiation atmosphere with the Hawking temperature T_BH~1/(8 \pi M) that is increasingly blueshifted as r approaches 2M. However, there is no horizon at the Schwarzschild radius. Instead, the fluid becomes increasingly hot and dense there, piling updoi:10.1103/physrevd.29.628 fatcat:zvjmpadadnbg7bpgn6hlua6dh4