Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes

Abstract

The present work extends our short communication Phys. Rev. Lett. 95, 111102 (2005). For smooth marginally outer trapped surfaces (MOTS) in a smooth spacetime we define stability with respect to variations along arbitrary vectors v normal to the MOTS. After giving some introductory material about linear non self-adjoint elliptic operators, we introduce the stability operator L_v and we characterize stable MOTS in terms of sign conditions on the principal eigenvalue of L_v. The main result shows that given a strictly stable MOTS S contained in one leaf of a given reference foliation in a spacetime, there is an open marginally outer trapped tube (MOTT), adapted to the reference foliation, which contains S. We give conditions under which the MOTT can be completed. Finally, we show that under standard energy conditions on the spacetime, the MOTT must be either locally achronal, spacelike or null.

arXiv comment33 pages, no figures, typos corrected, minor changes in presentation

References in corpus (13)

• General Laws of Black-Hole Dynamics
• Dynamical Horizons and their Properties
• Local existence of dynamical and trapping horizons
• Introduction to dynamical horizons in numerical relativity
• Marginally trapped tubes and dynamical horizons
• Spherically symmetric spacetimes with a trapped surface
• On the topology and area of higher dimensional black holes
• Non-symmetric trapped surfaces in the Schwarzschild and Vaidya spacetimes
• Area evolution, bulk viscosity and entropy principles for dynamical horizons
• On the existence of initial data containing isolated black holes
• Asymptotic Behavior of Spherically Symmetric Marginally Trapped Tubes
• Curvature estimates for stable marginally trapped surfaces
• Isolated and dynamical horizons from a common perspective

Cited by in corpus (5)

• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• Some remarks on the size of bodies and black holes
• A fast stroboscopic spectral method for rotating systems in numerical relativity
• Null hypersurfaces and trapping horizons
• A2: Mathematical relativity and other progress in classical gravity theory - a session report