The existence and stability of marginally trapped surfaces

Abstract

Marginally outer trapped surfaces (MOTSs, or marginal surfaces in short) are routinely used in numerical simulations of black hole spacetimes. They are an invaluable tool for locating and characterizing black holes quasi-locally in real time while the simulation is ongoing. It is often believed that a MOTS can behave unpredictably under time evolution; an existing MOTS can disappear, and a new one can appear without any apparent reason. In this paper we show that in fact the behavior of a MOTS is perfectly predictable and its behavior is dictated by a single real parameter, the \emph{stability parameter}, which can be monitored during the course of a numerical simulation. We demonstrate the utility of the stability parameter to fully understand the variety of marginal surfaces that can be present in binary black hole initial data. We also develop a new horizon finder capable of locating very highly distorted marginal surfaces and we show that even in these cases, the stability parameter perfectly predicts the existence and stability of marginal surfaces.

21 pages, 18 figures

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Cited by in corpus (22)

• Quasinormal modes and their overtones at the common horizon in a binary black hole merger
• The interior of a binary black hole merger
• Self-intersecting marginally outer trapped surfaces
• What Happens to Apparent Horizons in a Binary Black Hole Merger?
• End point of nonaxisymmetric black hole instabilities in higher dimensions
• Ultimate fate of apparent horizons during a binary black hole merger II: Horizons weaving back and forth in time
• MOTS in Schwarzschild: multiple self-intersections and extreme mass ratio mergers
• Horizons in a binary black hole merger I: Geometry and area increase
• Quasi-Local Black Hole Horizons: Recent Advances
• Twist-free axisymmetric critical collapse of a complex scalar field
• Exotic marginally outer trapped surfaces in rotating spacetimes of any dimension
• Inside the Final Black Hole: Puncture and Trapped Surface Dynamics
• Eigenvalues of the MOTS stability operator for slowly rotating Kerr black holes
• Geometric horizons in binary black hole mergers
• Properties of Quasi-local mass in binary black hole mergers
• Marginally Outer Trapped Tori in Black Hole Spacetimes
• Twist and higher modes of a complex scalar field at the threshold of collapse
• Ultimate fate of apparent horizons during a binary black hole merger I: Locating and understanding axisymmetric marginally outer trapped surfaces
• Dynamical Horizon Segments and Spacetime Isometries
• Revisiting the apparent horizon finding problem with multigrid methods
• Curvature Invariants and the Geometric Horizon Conjecture in a Binary Black Hole Merger
• The Interior MOTSs of Spherically Symmetric Black Holes