Vacuum handles carrying angular momentum; electrovac handles carrying net charge

Nonsimply-connected spacetimes can have locally defined Killing vectors that are globally defined only up to sign (pseudovectors). We show the existence of asymptotically flat vacuum spacetimes which are axisymmetric (have a rotational Killing pseudovector), are topologically trivial outside a spatially compact region, and which nevertheless have nonzero angular momentum. An analogous construction establishes the existence of source-free Einstein–Maxwell spacetimes which are topologically trivial outside a spatially compact region and which nevertheless carry nonzero net electric charge. The existence of such spacetimes leads to a new variant of the combined positive energy-cosmic-censorship conjecture: Given an asymptotically flat vacuum or electrovac initial data set which is axisymmetric and geodesically complete, the asymptotic mass, charge Q, and angular momentum J satisfy m?[Q2+(J/m)2]1/2.