Conserved charges in general relativity
Abstract
We present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved spacetime with Killing vectors. This definition enables us to define energy and momentum for matter by the volume integral. As a result we can compute charges of Schwarzschild and BTZ black holes by the volume integration of a delta function singularity. Employing the definition we also compute the total energy of a static compact star. It contains both the gravitational mass known as the Misner-Sharp mass in the Oppenheimer-Volkoff equation and the gravitational binding energy. We show that the gravitational binding energy has the negative contribution at maximum by 68% of the gravitational mass in the case of a constant density. We finally comment on a definition of generators associated with a vector field on a general curved manifold.
Keywords
Cite
@article{arxiv.2005.13233,
title = {Conserved charges in general relativity},
author = {Sinya Aoki and Tetsuya Onogi and Shuichi Yokoyama},
journal= {arXiv preprint arXiv:2005.13233},
year = {2021}
}
Comments
16 pages (single column), v3 (major revision): more discussion on a compact star included, a comparison with previous results given in the appendix, more references added