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.Comment: 23 pages, 14 figure
