Remarks on mass and angular momenta for $U(1{)}^2$-invariant initial data

Abstract

We extend Brill's positive mass theorem to a large class of asymptotically flat, maximal, $U(1{)}^2$-invariant initial data sets on simply connected four dimensional manifolds $\Sigma$. Moreover, we extend the local mass angular momenta inequality result Ref [1] for $U(1{)}^2$ invariant black holes to the case with nonzero stress energy tensor with positive matter density and energy-momentum current invariant under the above symmetries.

17 pages, LaTeX; v2. assumptions on generalized Brill data weakened and the main theorem modified accordingly

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Cited by in corpus (1)

• Geometrical inequalities bounding angular momentum and charges in General Relativity