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 [A. Alaee and H. K. Kunduri, Classical Quantum Gravity 32(16), 165020 (2015)] 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.

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