1112.2966 (László B. Szabados)

Mass, gauge conditions and spectral properties of the Sen-Witten and
3-surface twistor operators in closed universes    [PDF]

László B. Szabados

A non-negative expression, built from the norm of the 3-surface twistor operator and the energy-momentum tensor of the matter fields on a spacelike hypersurface, is found which, in the asymptotically flat/hyperboloidal case, provides a lower bound for the ADM/Bondi--Sachs mass, while on closed hypersurfaces it gives the first eigenvalue of the Sen--Witten operator. Also in the closed case, its vanishing is equivalent to the existence of non-trivial solutions of Witten's gauge condition. Moreover, it is vanishing if and only if the closed data set is in a flat spacetime with toroidal spatial topology. Thus it provides a positive definite measure of the strength of the gravitational field (with physical dimension mass) on closed hypersurfaces, i.e. some sort of the total mass of closed universes.

View original: http://arxiv.org/abs/1112.2966