Abstract
It was recently pointed out by Barrau, Martineau and Renevey that the mass of the Schwarzschild black hole immersed in a heat bath tends to infity in a finite time. We show that this singularity problem in the black hole mass may be avoided, if the stretched horizon of the black hole is constructed out of a fixed, finite number of discrete constituents, and an appropriate counting is applied to the energy eigenstates of the hole.
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