Growth of a Black Hole on a Self-Gravitating Radiation

We feed a black hole on a self-gravitating radiation and observe what happens during the process. Considering a spherical shell of radiation, we show that the contribution of self-gravity makes the thermodynamic interaction through the bottom of the shell be distinguished from thermodynamic interaction through its top. The growth of a black hole horizon appears to be a sudden jump rather than a sequential increase. We additionally show that much of the entropy will be absorbed into the black hole only at the last moment of the collapse.Comment: title changed, 6 pages, no figure