Spin Entropy for Kerr Black Holes

Abstract

It is known that the entropy for a singular spacetime metric can be calculated in the framework of classical field theories by applying Noether's theorem to stationary solutions of Einstein's field equations, integrating a suitable form on a trapping surface for the singularity. When the Kerr solution is considered, two different horizons appear. The physical entropy for the system is well known to be related to the outer horizon. We investigate here which is the meaning of the entropy calculated (via first principle of black hole thermodynamics) on the inner horizon. We show that this entropy, which was earlier interpreted as a sort of "spin entropy" of the black hole, admits in fact an interpretation as a quantity associated to a conserved charge which is related to the rotational degrees of freedom of the system.