Event Horizon Deformations in Extreme Mass-Ratio Black Hole Mergers

TL;DR

This paper analyzes how the event horizon of a large black hole deforms during a merger with a small compact object, using perturbation theory and null geodesic propagation to characterize the horizon geometry and area increase.

Contribution

It provides an analytic description of event horizon deformations and caustic formation in extreme mass-ratio black hole mergers, focusing on large-l perturbations near the caustic.

Findings

Existence of a caustic before the merger

Large-l perturbations dominate near the caustic

Half of the horizon area increase is due to generators entering through the caustic

Abstract

We study the geometry of the event horizon of a spacetime in which a small compact object plunges into a large Schwarzschild black hole. We first use the Regge-Wheeler and Zerilli formalisms to calculate the metric perturbations induced by this small compact object, then find the new event horizon by propagating null geodesics near the unperturbed horizon. A caustic is shown to exist before the merger. Focusing on the geometry near the caustic, we show that it is determined predominantly by large-l perturbations, which in turn have simple asymptotic forms near the point at which the particle plunges into the horizon. It is therefore possible to obtain an analytic characterization of the geometry that is independent of the details of the plunge. We compute the invariant length of the caustic. We further show that among the leading-order horizon area increase, half arises from generators that enter the horizon through the caustic, and the rest arises from area increase near the caustic, induced by the gravitational field of the compact object.