Apparent horizons in D-dimensional Robinson-Trautman spacetime
Otakar Svitek
TL;DR
This paper generalizes the Penrose-Tod equation for apparent horizons to higher-dimensional Robinson-Trautman spacetimes, proving existence and uniqueness results in four dimensions with a cosmological constant.
Contribution
It extends previous four-dimensional results to higher dimensions and includes cases with a nonvanishing cosmological constant.
Findings
Generalized Penrose-Tod equation for D-dimensional spacetimes
Proved existence and uniqueness of solutions in four dimensions
Extended Tod's results to include cosmological constant cases
Abstract
We derive the higher dimensional generalization of Penrose-Tod equation describing apparent horizons in Robinson-Trautman spacetimes. New results concerning the existence and uniqueness of its solutions in four dimensions are proven. Namely, previous results of Tod are generalized to nonvanishing cosmological constant.
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