Black hole thermodynamics without a black hole?

Abstract

In the present paper we consider, using our earlier results, the process of quantum gravitational collapse and argue that there exists the final quantum state when the collapse stops. This state, which can be called the “no-memory state”, reminds the final “no-hair state” of the classical gravitational collapse. Translating the “no-memory state” into classical language we construct the classical analogue of quantum black hole and show that such a model has a topological temperature which equals exactly the Hawking's temperature. Assuming for the entropy the Bekenstein–Hawking value we develop the local thermodynamics for our model and show that the entropy is naturally quantized with the equidistant spectrum S+ γ 0 N. Our model allows, in principle, to calculate the value of γ 0. In the simplest case, considered here, we obtain γ 0=ln2.