The Interior MOTSs of Spherically Symmetric Black Holes

TL;DR

This paper investigates the existence and properties of self-intersecting marginally outer trapped surfaces (MOTSs) inside static, spherically symmetric black holes, revealing how inner horizons influence their behavior and connecting findings to binary black hole mergers.

Contribution

It introduces a parametrized family of Painlevé-Gullstrand-like coordinates to analyze MOTSs, demonstrating their generic presence and properties in various black hole interiors, including Reissner-Nordström and Gauss-Bonnet black holes.

Findings

Self-intersecting MOTSs are generic in Schwarzschild spacetime.

Inner horizons lead to a finite number of self-intersecting MOTSs.

Properties of MOTSs depend on the black hole's interior structure.

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{\'e}-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-Nordstr\"om 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.