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Conserved charges in general relativity

Aoki, Sinya Onogi, Tetsuya Yokoyama, Shuichi 京都大学 DOI:10.1142/s0217751x21500986

2021.04

概要

We present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved space–time 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.

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by KYOTO UNIVERSITY on 11/05/21. Re-use and distribution is strictly not permitted, except for Open Access articles.

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