Conserved charges in general relativity

• Aoki, Sinya

  Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University

• Onogi, Tetsuya

  Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University; Department of Physics, Osaka University

• Yokoyama, Shuichi

  Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University

Abstract

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.

Journal

• International Journal of Modern Physics A

  International Journal of Modern Physics A 36 (10), 2150098-, 2021-04

  World Scientific Pub Co Pte Lt

Keywords

• Field theory on curved space–time
• conserved charge
• black hole
• general relativity
• energy–momentum tensor
• compact star
• Oppenheimer–Volkoff equation

Details

• CRID: 1050290229622097664
• NII Article ID: 120007171020
• DOI: 10.1142/s0217751x21500986
• ISSN: 1793656X
• ISSN: 0217751X
• HANDLE: 2433/266162
• Web Site: https://www.worldscientific.com/doi/pdf/10.1142/S0217751X21500986
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN