Quasi-Local Conservation Equations in General Relativity

Abstract

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.

RevTex, 8 pages, a final version to appear in Phys. Lett. A

References in corpus (6)

• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Gravitational Energy in Spherical Symmetry
• Quasi-Local Gravitational Energy
• Two dimensional Sen connections and quasi-local energy-momentum
• Kaluza-Klein Formalism of General Spacetimes
• (2,2)-Formalism of General Relativity: An Exact Solution

Cited by in corpus (2)

• New Hamiltonian formalism and quasi-local conservation equations of general relativity
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