Spinor derivation of quasilocal mean curvature mass in General Relativity
Mathematical Physics
2013-10-31 v1 High Energy Physics - Theory
math.MP
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.
Keywords
Cite
@article{arxiv.1310.8199,
title = {Spinor derivation of quasilocal mean curvature mass in General Relativity},
author = {Stephen C. Anco},
journal= {arXiv preprint arXiv:1310.8199},
year = {2013}
}