Trapped surfaces

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.

32 pages, 12 figures, 3 Tables. Invited course at the 2011 Shanghai Asia-Pacific School and Workshop on Gravitation, version submitted to the Proceedings. Minor typos corrected

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• Black Hole Horizons from the Double Copy
• Algorithms for the explicit computation of Penrose diagrams
• A critical appraisal of the singularity theorems
• Geometric surfaces: An invariant characterization of spherically symmetric black hole horizons and wormhole throats
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• A dual null formalism for the collapse of fluids in a cosmological background
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• A non-local way around the no-global-symmetries conjecture in quantum gravity?
• Revisiting the Birkhoff theorem from a dual null point of view
• Nonlocal modification of the Kerr metric
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• The marginally trapped surfaces in spheroidal spacetimes
• An Invariant Characterization of the Levi-Civita Spacetimes
• Geometric horizons in binary black hole mergers
• Feasibility of singularity avoidance for a collapsing object due to a scalar field
• On the hypotheses of Penrose's singularity theorem under disformal transformations
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• A concise introduction to trapped surface formation in general relativity
• Ultra-massive spacetimes in 2+1 dimensions with positive Λ
• Alternative characterization of a black hole boundary
• Expansion of bundles of light rays in the Lemaître -- Tolman models
• Black holes and their horizons in semiclassical and modified theories of gravity
• On complete trapped submanifolds in globally hyperbolic spacetimes