Classification of spacelike surfaces in spacetime

Abstract

A classification of 2-dimensional surfaces imbedded in spacetime is presented, according to the algebraic properties of their shape tensor. The classification has five levels, and provides among other things a refinement of the concepts of trapped, umbilical and extremal surfaces, which split into several different classes. The classification raises new important questions and opens many possible new lines of research. These, together with some applications and examples, are briefly considered.

42 pages, 10 tables, many diagrams

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• General Laws of Black-Hole Dynamics
• Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws
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Cited by in corpus (17)

• The 1965 Penrose singularity theorem
• Present status of the Penrose inequality
• The region with trapped surfaces in spherical symmetry, its core, and their boundaries
• Trapped surfaces
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• A Reformulation of the Hoop Conjecture
• Boost invariant marginally trapped surfaces in Minkowski 4-space
• Stability of marginally outer trapped surfaces and symmetries
• New Examples of Marginally Trapped Surfaces and Tubes in Warped Spacetimes
• Painlevé-Gullstrand synchronizations in spherical symmetry
• Unstable marginally outer trapped surfaces in static spherically symmetric spacetimes
• Marginally trapped surfaces in Minkowski 4-space invariant under a rotation subgroup of the Lorentz group
• Scalar lumps with a horizon
• On the Resilience of Black Hole Evaporation: Gravitational Tunneling through Universal Horizons
• Spacetime characterizations of $\Lambda$-vacuum metrics with a null Killing 2-form
• Involute, minimal, outer and increasingly trapped surfaces
• Uniqueness theorems for static spacetimes containing marginally outer trapped surfaces