Localization of energy for a Kerr black hole

Abstract

In the teleparallel equivalent of general relativity the energy density of asymptoticaly flat gravitational fields can be naturally defined as a scalar density restricted to a three dimensional spacelike hypersurface. The scalar density has simple expression in terms of the trace of the torsion tensor. Here we obtain the formal expression of the localized energy for a Kerr black hole. The energy inside a surface of constant radius can be explicitly calculated in the limit of small $a$, the specific angular momentum. Such expression turns out to be exactly the same as the one obtained by means of the method recently proposed by Brown and York.