Vacuum initial data, singularities, and cosmic censorship

Abstract

The formation of a naked singularity in a vacuum, asymptotically flat spacetime would be a clear violation of cosmic censorship. We find initial value solutions to Einstein's field equations that may lead to this behavior. We construct two families of asymptotically flat, axisymmetric vaccum solutions at a moment of time symmetry. The limiting members of these families are singular. Our first family represents a linear string of Schwarzschild black holes. We study the divergence of the gravitational tidal field outside the holes as their number along the string is increased. Our second family consists of prolate Brill gravitational wave packets. We examine the tidal field strength as the characteristic width of the wave is reduced towards zero. In both cases we find that configurations can be constructed with arbitrarily large fields that are not clothed by apparent horizons. These configurations are characterized by long, prolate concentrations of mass energy. We analyze our results in the context of the hoop conjecture.