Trapped surfaces, horizons and exact solutions in higher dimensions

TL;DR

This paper introduces a purely geometric criterion for identifying trapped surfaces in arbitrary higher-dimensional Lorentzian manifolds, with applications to horizons, solution classification, and dimensional reductions in gravitational theories.

Contribution

It provides a simple, theory-independent geometric condition for trapped surfaces, applicable to various physical contexts including black holes, rings, and higher-dimensional theories.

Findings

A universal criterion for trapped surfaces in higher dimensions.

Application to defining horizons in diverse gravitational solutions.

Conditions for the absence of closed trapped surfaces.

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.