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(1+1)-dimensional formalism and quasi-local conservation equations

Jong Hyuk Yoon
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Abstract

A set of exact quasi-local conservation equations is obtained in the (1+1)-dimensional description of the Einstein's equations of (3+1)-dimensional spacetimes. These equations are interpreted as quasi-local energy, linear momentum, and angular momentum conservation equations. In the asymptotic region of asymptotically flat spacetimes, it is shown that these quasi-local conservation equations reduce to the conservation equations of Bondi energy, linear momentum, and angular momentum, respectively. When restricted to the quasi-local horizon of a generic spacetime, which is defined without referring to the infinity, the quasi-local conservation equations coincide with the conservation equations on the stretched horizon studied by Price and Thorne. All of these quasi-local quantities are expressed as invariant two-surface integrals, and geometrical interpretations in terms of the area of a given two-surface and a pair of null vector fields orthogonal to that surface are given.

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Jong Hyuk Yoon. 2002-12-09. (1+1)-dimensional formalism and quasi-local conservation equations. https://arxiv.org/abs/gr-qc/0212042

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