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In recent years, gravitational-wave astronomy has motivated increasinglyaccurate perturbative studies of gravitational dynamics in compact binaries.This in turn has enabled more detailed analyses of the dynamical black holes inthese systems. For example, Pound et al. [Phys. Rev. Lett. 124, 021101 (2020)]recently computed the surface area of a Schwarzschild black hole's apparenthorizon, perturbed by an orbiting body, to second order in the binary's massratio. In this paper, we take that as the starting point for a comprehensivestudy of a perturbed Schwarzschild black hole's apparent and event horizon atsecond perturbative order, deriving generic formulas for the first- andsecond-order corrections to the horizons' radial profiles, surface areas,Hawking masses, and intrinsic curvatures. We find that the two horizons areremarkably similar, and that any teleological behavior of the event horizon issuppressed in several ways. Critically, we establish that at all orders, theperturbed event horizon in a small-mass-ratio binary is effectively localizedin time. Even more pointedly, the event horizon is identical to the apparenthorizon at linear order regardless of the source of perturbation, implying thatthe seemingly teleological "tidal lead", previously observed in linearlyperturbed event horizons, is not genuinely teleological in origin. The twohorizons do generically differ at second order, but their Hawking masses remainidentical, implying that the event horizon obeys the same energy-flux balancelaw as the apparent horizon. At least in the case of a binary system, thedifference between their surface areas remains extremely small even in the latestages of inspiral. In the course of our analysis, we also numericallyillustrate puzzling behaviour in the black hole's motion around the binary'scenter of mass.

Deformed Schwarzschild horizons in second-order perturbation theory: mass, geometry, and teleology