ON THE GLOBAL STRUCTURE OF ROBINSON-TRAUTMAN SPACE-TIMES

The global structure of Robinson-Trautman space-times is studied. When the space-time topology is R+ x R x S2 it is shown that all Robinson-Trautman space-times can be C117 extended (in the vacuum Robinson-Trautman class of metrics) beyond the r = 2m 'Schwarzschild-like' event horizon; evidence is given supporting the conjecture, that no smooth extensions beyond the r = 2m event horizon exist unless the metric is the Schwarzschild one. When the space-time topology is R+ x R x 2M, with 2M a higher genus surface, and the mass parameter m is negative, Schwarzschild-like event horizons are shown to occur. The proofs of these results are based on the derivation of a detailed asymptotic expansion describing the long-time behaviour of the solutions of a nonlinear parabolic equation.