Trapped surfaces and symmetries

Abstract

We prove that strictly stationary spacetimes cannot contain closed trapped nor marginally trapped surfaces. The result is purely geometric and holds in arbitrary dimension. Other results concerning the interplay between (generalized) symmetries and trapped submanifolds are also presented.

9 pages, no figures. Final corrected version to appear in Class. Quantum Grav

References in corpus (2)

• Singularity Theorems and Their Consequences
• Causal symmetries

Cited by in corpus (36)

• Local existence of dynamical and trapping horizons
• 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
• Black holes and black hole thermodynamics without event horizons
• Singularity theorems based on trapped submanifolds of arbitrary co-dimension
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• A Reformulation of the Hoop Conjecture
• On the existence of horizons in spacetimes with vanishing curvature invariants
• Classification of spacelike surfaces in spacetime
• Evolving black holes from conformal transformations of static solutions
• Boost invariant marginally trapped surfaces in Minkowski 4-space
• Fundamental properties and applications of quasi-local black hole horizons
• Review on exact and perturbative deformations of the Einstein-Straus model: uniqueness and rigidity results
• Stability of marginally outer trapped surfaces and symmetries
• On marginally outer trapped surfaces in stationary and static spacetimes
• New Examples of Marginally Trapped Surfaces and Tubes in Warped Spacetimes
• A critical appraisal of the singularity theorems
• Quasi-Local Black Hole Horizons: Recent Advances
• A note on the uniqueness of global static decompositions
• A dual null formalism for the collapse of fluids in a cosmological background
• Charged cosmological black holes: a thorough study of a family of solutions
• A gravitational collapse singularity theorem consistent with black hole evaporation
• Marginally trapped surfaces in Minkowski 4-space invariant under a rotation subgroup of the Lorentz group
• Symmetry and instability of marginally outer trapped surfaces
• Where are the trapped surfaces?
• Geometry of normal graphs in Euclidean space and applications to the Penrose inequality in Minkowski
• Scalar lumps with a horizon
• Extremal and weakly trapped submanifolds in Generalized Robertson-Walker spacetimes
• Gradient conformal stationarity and the CMC condition in LRS spacetimes
• Dynamical Horizon Segments and Spacetime Isometries
• Nonsingular spherically symmetric black-hole model with holonomy corrections
• On complete trapped submanifolds in globally hyperbolic spacetimes
• Ultra-massive spacetimes in 2+1 dimensions with positive Λ
• Dynamical axisymmetric compact objects in General Relativity