Evolution of time-symmetric gravitational waves: Initial data and apparent horizons

Abstract

Initial data were constructed numerically representing pure gravitational radiation with no sources or wormholes, under the conditions of time symmetry, axisymmetry, vacuum, and no rotation. The constraints were solved by making a conformal transformation on a base metric and solving the scale equation for the conformal factor. The initial data contain a black hole if the amplitude of the waves is sufficiently strong. The locations of apparent horizons were found for several such amplitudes. At a critical amplitude the throat pinches off and the geometry becomes singular.