# Topology of Black Hole Binary-Single Interactions

## TL;DR

This study explores how the outcomes of binary-single black hole interactions depend on initial conditions, revealing the potential for multiple gravitational wave mergers, including scenarios observable by LIGO, especially in co-planar configurations.

## Contribution

The paper introduces a comprehensive analysis of the topology of black hole interactions using extensive N-body simulations that include gravitational wave emission, highlighting the possibility of sequential GW mergers.

## Key findings

- Co-planar interactions often lead to rapid sequential GW mergers.
- Inclusion of GW emission in simulations reveals new merger pathways.
- Some interactions produce events observable by LIGO within short timescales.

## Abstract

We present a study on how the outcomes of co-planar binary-single black hole (BH) interactions distribute as a function of the orbital initial conditions. We refer to this distribution as the topology. Using an $N$-body code that includes BH finite sizes and gravitational wave (GW) emission in the equation-of-motion (EOM), we perform more than a million three-body scatterings to explore the topology of both the classical and the relativistic limit. We further describe how the inclusion of GW emission in the EOM naturally leads to scenarios where the binary-single system undergoes two successive GW mergers. The time span from the first to the second GW merger is shortest in co-planar interactions, and are for some configurations even short enough for LIGO to observe both events. We note that co-planar interactions could be frequent in environments such as active galactic nuclei discs.