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arXiv · 0911.5317

Past horizons in Robinson-Trautman spacetimes with a cosmological constant

Jiri Podolsky·Otakar Svitek
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Abstract

We study past horizons in the class of type II Robinson-Trautman vacuum spacetimes with a cosmological constant. These exact radiative solutions of Einstein's equations exist in the future of any sufficiently smooth initial data, and they approach the corresponding spherically symmetric Schwarzschild-(anti-)de Sitter metric. By analytic methods we investigate the existence, uniqueness, location and character of the past horizons in these spacetimes. In particular, we generalize the Penrose-Tod equation for marginally trapped surfaces, which form such white-hole horizons, to the case of a nonvanishing cosmological constant, we analyze behavior of its solutions and visualize their evolutions. We also prove that these horizons are explicit examples of an outer trapping horizon and a dynamical horizon, so that they are spacelike past outer horizons.

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Jiri Podolsky, Otakar Svitek. 2009-11-27. Past horizons in Robinson-Trautman spacetimes with a cosmological constant. https://doi.org/10.1103/physrevd.80.124042

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