# Deformation of horizons during a merger

## TL;DR

This paper models the deformation of black hole horizons during an extreme mass ratio merger by numerically evolving perturbations and analyzing the horizon geometry, providing insights into horizon dynamics during such events.

## Contribution

It introduces a numerical approach using the Zerilli formalism to study horizon deformation in EMR mergers, including horizon geometry analysis.

## Key findings

- Horizon deformation patterns during merger are characterized.
- Apparent horizon geometry is analyzed in detail.
- Numerical evolution of perturbations is successfully implemented.

## Abstract

We model an extreme mass ratio merger (EMR) as a point particle radially plunging into a large Schwarzschild black hole. We assume that the mass of the point particle, $\mu$, is much smaller than the black hole mass M. Under this assumption we can employ the Zerilli formalism modified to include a source term which arises from the energy-momentum tensor of the small object. We solve the Zerilli equation by numerically evolving initial data. Then, we ray trace the null geodesics of the event horizon from after the merger backward in time to extract the geometry of the perturbed event horizon. Further, we take advantage of the axisymmetry of the setup to locate the apparent horizon and study its geometry.