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arXiv · 1310.8199

Spinor derivation of quasilocal mean curvature mass in General Relativity

Stephen C. Anco
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Abstract

A spinor derivation is presented for quasilocal mean-curvature mass of spacelike 2-surfaces in General Relativity. The derivation is based on the Sen-Witten spinor identity and involves the introduction of novel nonlinear boundary conditions related to the Dirac current of the spinor at the 2-surface and the tangential flux of a boundary Dirac operator, as well the use of a spin basis adapted to the mean curvature frame of the 2-surface normal space. This setting may provide an alternative approach to a positivity proof for mean-curvature mass based on showing that Witten's equation admits a spinor solution satisfying the proposed nonlinear boundary conditions.

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Stephen C. Anco. 2013-10-30. Spinor derivation of quasilocal mean curvature mass in General Relativity. https://arxiv.org/abs/1310.8199

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