Radial geodesics as a microscopic origin of black hole entropy . II : Features of Reissner – Nordstrøm black hole

Radial geodesics as a microscopic origin of black hole entropy. Abstract. The entropy of charged black hole is calculated by using the partition function evaluated at radial geodesics confined under horizons. We establish two quantum phase states inside the black hole and a transition between them. The second chapter of present paper is devoted to consequent launching the constructed vehicle to a charged black hole. The Reissner–Nordstrøm black hole has got two horizons, that constitutes a source of specific properties: We will show that the thermal quantization leads to i) quantizing a ratio of horizon areas, ii) two states of aggregation with different temperatures and entropies, iii) a possibility of phase transition between two states. We derive the entropy of Reissner-Nordstrøm black hole in terms of partition function evaluated by the action for causal radial geodesics confined under the horizons. The interior structure of charged black hole mathematically differs from that of Schwarzschild one: instead of conic geometry with a single map on the manifold it has got a sphere, which should be covered by two coordinated maps. In section 2 we describe the mapping of causal radial geodesics confined under the horizon and thermally quantize them. Section 3 is devoted to the evaluation of entropy. Results are summarized in section 4.