Ultimate fate of apparent horizons during a binary black hole merger I: Locating and understanding axisymmetric marginally outer trapped surfaces

TL;DR

This paper introduces new numerical tools to locate and analyze the evolution of marginally outer trapped surfaces during binary black hole mergers, providing insights into the fate of initial horizons in axisymmetric scenarios.

Contribution

It presents a novel shooting-method for finding axisymmetric MOTSs and reinterprets the stability operator, advancing understanding of black hole horizon evolution.

Findings

New method effectively locates MOTSs in axisymmetric spacetimes

Reinterpretation of stability operator as Jacobi equation

Preliminary results on exact solutions and initial data

Abstract

In classical numerical relativity, marginally outer trapped surfaces (MOTSs) are the main tool to locate and characterize black holes. For five decades it has been known that during a binary merger, a new outer horizon forms around the initial apparent horizons of the individual holes once they are sufficiently close together. However the ultimate fate of those initial horizons has remained a subject of speculation. Recent axisymmetric studies have shed new light on this process and this pair of papers essentially completes that line of research: we resolve the key features of the post-swallowing axisymmetric evolution of the initial horizons. This first paper introduces a new shooting-method for finding axisymmetric MOTSs along with a reinterpretation of the stability operator as the analogue of the Jacobi equation for families of MOTSs. Here, these tools are used to study exact solutions and initial data. In the sequel paper they are applied to black hole mergers.