Trapped surfaces, horizons and exact solutions in higher dimensions

Abstract

A very simple criterion to ascertain if (D-2)-surfaces are trapped in arbitrary D-dimensional Lorentzian manifolds is given. The result is purely geometric, independent of the particular gravitational theory, of any field equations or of any other conditions. Many physical applications arise, a few shown here: a definition of general horizon, which reduces to the standard one in black holes/rings and other known cases; the classification of solutions with a (D-2)-dimensional abelian group of motions and the invariance of the trapping under simple dimensional reductions of the Kaluza-Klein/string/M-theory type. Finally, a stronger result involving closed trapped surfaces is presented. It provides in particular a simple sufficient condition for their absence.

7 pages, no figures, final version to appear in Class. Quantum Grav

References in corpus (4)

• A rotating black ring in five dimensions
• Gravitational Energy in Quadratic Curvature Gravities
• Generalized Weyl Solutions
• Singularity Theorems and Their Consequences

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