The Interior MOTSs of Spherically Symmetric Black Holes

Abstract

There are notable similarities between the marginally outer trapped surfaces (MOTSs) present in the interior of a binary black hole merger and those present in the interior of the Schwarzschild black hole. Here we study the existence and properties of MOTSs with self-intersections in the interior of more general static and spherically symmetric black holes and coordinate systems. Our analysis is carried out in a parametrized family of Painlev{é}-Gullstrand-like coordinates that we introduce. First, for the Schwarzschild spacetime, we study the existence of these surfaces for various slicings of the spacetime finding them to be generic within the family of coordinate systems we investigate. Then, we study how an inner horizon affects the existence and properties of these surfaces by exploring examples: the Reissner-Nordström black hole and the four-dimensional Gauss-Bonnet black hole. We find that an inner horizon results in a finite number of self-intersecting MOTSs, but their properties depend sensitively on the interior structure of the black hole. By analyzing the spectrum of the stability operator, we show that our results for two-horizon black holes provide exact-solution examples of recently observed properties of unstable MOTSs present in the interior of a binary black hole merger, such as the sequence of bifurcations/annihilations that lead to the disappearance of apparent horizons.

arXiv comment19 pages, 17 figures

References in corpus (25)

• Isolated and dynamical horizons and their applications
• Einstein-Gauss-Bonnet gravity in 4-dimensional space-time
• Dynamical Horizons and their Properties
• Introduction to Isolated Horizons in Numerical Relativity
• Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws
• Horndeski Gravity as $D\to 4$ Limit of Gauss-Bonnet
• Local existence of dynamical and trapping horizons
• Regular coordinate systems for Schwarzschild and other spherical spacetimes
• On Taking the $D\to 4$ limit of Gauss-Bonnet Gravity: Theory and Solutions
• Derivation of Regularized Field Equations for the Einstein-Gauss-Bonnet Theory in Four Dimensions
• Production and decay of evolving horizons
• Marginally trapped tubes and dynamical horizons
• Decoding the Apparent Horizon: A Coarse-Grained Holographic Entropy
• Physical observability of horizons
• The Penrose inequality and apparent horizons
• Dynamics of marginally trapped surfaces in a binary black hole merger: Growth and approach to equilibrium
• The interior of a binary black hole merger
• What can the quantum liquid say on the brane black hole, the entropy of extremal black hole and the vacuum energy?
• The existence and stability of marginally trapped surfaces
• Self-intersecting marginally outer trapped surfaces
• What Happens to Apparent Horizons in a Binary Black Hole Merger?
• Ultimate fate of apparent horizons during a binary black hole merger II: Horizons weaving back and forth in time
• Generalized Painlevé-Gullstrand metrics
• MOTS in Schwarzschild: multiple self-intersections and extreme mass ratio mergers
• Horizons in a binary black hole merger I: Geometry and area increase