Particle dynamics around a tidally deformed black hole

The Kerr geometry provides the standard leading-order description of isolated astrophysical black holes, but realistic black holes are generically subject to environmental perturbations. Such perturbations can be particularly relevant for long-lived orbital systems, including extreme-mass-ratio inspirals in the presence of a nearby third body.

In this talk, I will present recent and ongoing work on particle motion around a tidally deformed black hole, with the tidal field sourced by an external companion. In particular, I will discuss how the integrable structure of bound Kerr geodesics breaks down as the tidal-field strength increases, the resulting phase-space signatures of resonant orbits, and the phase-space manifestations of transient tidal resonances.