Radial geodesics as a microscopic origin of black hole entropy

Abstract

Causal radial geodesics with a positive interval in the Schwarzschild metric include a subset of trajectories completely confined behind a horizon, which compose a thermal statistical ensemble with the Hawking-Gibbons temperature. The Bekenstein-Hawking entropy is given by an action at corresponding geodesics of particles with a summed mass equal to that of the black hole in the limit of a large mass. The entropy of a charged black hole is calculated in this way by using the partition function evaluated at radial geodesics confined behind horizons. We establish two quantum phase states inside the black hole and a transition between them. For the Kerr-Newman black hole we specify an angular motion on geodesics to reduce the problem to the case of radial motion elaborated on in previous papers. An appropriate value of entropy for a charged and rotating black hole is obtained by calculating the partition function on thermal geodesics confined behind horizons. The quantum aggregation is classified in a similar way to the Reissner-Nordstr\o{}m black hole.