Lower bounds for eigenvalues of the Dirac-Witten operator
The author obtains optimal lower bounds for the eigenvalues of the Dirac-Witten operator associated with a space-like hypersurface \(M\) of a Lorentzian manifold (with or without boundary), subject to certain conditions involving the mean curvature, the scalar curvature, and the spinor energy-momentum tensor. In the limiting case the space-like hypersurface is either a maximal Einstein manifold with positive scalar curvature, or a Ricci-flat manifold with non-zero constant mean curvature. Contents include: Introduction (containing a brief overview of the topic); Main results (statement and proofs when \(M\) is without a boundary); the corresponding cases when \(M\) has a boundary; an Example (the de Sitter spacetime imbedded in a 5-dimensional Minkowskian space-time); and References (containing 19 items).
space-like hypersurfaces of a Lorentzian manifold
scientific article; zbMATH DE number 5654010
scientific article