2000/04/30 by J. H. Yoon, Jong Hyuk Yoon · 1 citation
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #gr-qc
paper · pdf · doi:10.1016/s0375-9601(01)00756-3
published as Phys.Lett. A292 (2001) 166-172 · RevTex, 8 pages, a final version to appear in Phys. Lett. A
arxiv created 2001/11/21 · openalex publication_date 2001/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A set of exact quasi-local conservation equations is derived from the Einstein's equations using the first-order Kaluza-Klein formalism of general relativity in the (2,2)-splitting of 4-dimensional spacetime. These equations are interpreted as quasi-local energy, momentum, and angular momentum conservation equations. In the asymptotic region of asymptotically flat spacetimes, it is shown that the quasi-local energy and energy-flux integral reduce to the Bondi energy and energy-flux, respectively. In spherically symmetric spacetimes, the quasi-local energy becomes the Misner-Sharp energy. Moreover, on the event horizon of a general dynamical black hole, the quasi-local energy conservation equation coincides with the conservation equation studied by Thorne \it et al. We discuss the remaining quasi-local conservation equations briefly.