Black hole horizons during extreme mass ratio mergers

Abstract

A marginally outer trapped surface (MOTS) is a quasi-local alternative to the event horizon that captures the dynamical features of a black hole. Previously, Emparan and Martínez have shown that the evolution of the event horizon during extreme mass ratio (EMR) mergers can be solved exactly in the limit where the large black hole becomes infinite in extent. In this project, we studied the evolution of MOTS during EMR mergers in the same setup where MOTS can be locally approximated by spacelike open surfaces with vanishing null expansion in the Schwarzschild geometry. We defined these open surfaces as marginally outer trapped open surfaces (MOTOS), which can be fully determined by the local properties of spacetime. We studied axisymmetric MOTOS contained in constant time slices of Schwarzschild spacetimes in different coordinate systems. In the Painlevé-Gullstrand coordinate system, we found open and closed surfaces with an arbitrary number of self-intersections inside the Schwarzschild horizon. We also extrapolate these results to predict possible behaviours of MOTS during extreme mass ratio mergers based on previous numerical studies of the evolution of MOTS during black hole mergers.