We derive the higher-dimensional generalization of Penrose-Tod equation describing past horizon in Robinson-Trautman spacetimes with a cosmological constant and pure radiation. Existence of its solutions in D>4 dimensions is proved using tools for nonlinear elliptic partial differential equations. We show that this horizon is naturally a trapping and a dynamical horizon. The findings generalize results from D=4.
Physical Review D
- Pub Date:
- August 2011
- Spacetime topology causal structure spinor structure;
- Higher-dimensional black holes black strings and related objects;
- General Relativity and Quantum Cosmology;
- to appear in Phys. Rev. D