A lower bound for the eigenvalues of the Sen-Witten operator on closed spacelike hypersurfaces

Details A lower bound for the eigenvalues of the Sen-Witten operator on closed spacelike hypersurfaces A lower bound for the eigenvalues of the Sen-Witten operator on closed spacelike hypersurfaces

2007-12-17

arxiv.org/abs/0712.2785v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages

Scientific paper

The eigenvalue problem for the Sen--Witten operator on closed spacelike hypersurfaces is investigated. The (square of its) eigenvalues are shown to be given exactly by the 3-surface integral appearing in the expression of the total energy-momentum of the matter+gravity systems in Witten's energy positivity proof. A sharp lower bound for the eigenvalues, given in terms of the constraint parts of the spacetime Einstein tensor, i.e. the energy and momentum densities of the matter fields, is given.

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