PENROSE QUASI-LOCAL MASS IN A NUMERICALLY COMPUTED SPACE-TIME

We describe a numerical calculation of Penrose's quasilocal mass on a sequence of axisymmetric two-surfaces in the three-surface of time symmetry of a numerically constructed vacuum space-time corresponding to a Brill gravitational wave interacting with a Schwarzschild black hole. The resulting mass is positive, responds very sensitively to the presence of gravitational waves, and tends rapidly to the ADM mass outside the wave. The isoperimetric inequality for black holes and the hoop conjecture of Thorne are investigated with this definition of mass.