Trapped surfaces

TL;DR

This paper reviews the concept of trapped surfaces in general relativity, exploring their properties, interactions with spacetime structures, and implications for black hole definitions and horizons.

Contribution

It provides a comprehensive overview of trapped surfaces, including their global properties, interactions with vector fields, and applications to black hole boundaries and horizons.

Findings

Trapped surfaces exhibit 'clairvoyance' and can enter flat spacetime regions.

Results on the interaction of trapped surfaces with vector fields and hypersurfaces.

Discussion of marginally trapped tubes, trapping horizons, and trapped region boundaries.

Abstract

I review the definition and types of (closed) trapped surfaces. Surprising global properties are shown, such as their "clairvoyance" and the possibility that they enter into flat portions of the spacetime. Several results on the interplay of trapped surfaces with vector fields and with spatial hypersurfaces are presented. Applications to the quasi-local definition of Black Holes are discussed, with particular emphasis set onto marginally trapped tubes, trapping horizons and the boundary of the region with closed trapped surfaces. Finally, the core of a trapped region is introduced, and its importance discussed.