Dissipation due to the (not-so) conservative self-force for resonant extreme-mass-ratio inspirals

The inspiral of a small compact object into a massive black hole, or an extreme-mass-ratio inspiral (EMRI), is often modeled using self-force theory. In self-force theory, a small body orbiting in a stationary gravitational background experiences a self-force due its own perturbing (gravitational, scalar, and/or electromagnetic) field. This self-force, in turn, sources the small body's motion. One often separates this self-force into two pieces: a (time-antisymmetric) dissipative component, which is responsible for the inspiral, and a (time-symmetric) conservative component, which typically perturbs the small body's orbit without driving its inspiral. However, using a scalar model, we numerically demonstrate that when a scalar point-charge enters a resonant orbit about a Kerr black hole (i.e., its radial and polar orbital frequencies form a rational ratio), the conservative scalar self-force becomes not-so conservative and can contribute to the dissipation of the Carter constant, thus driving the system away from the resonance. We analyze the strength of the conservative self-force contributions for different resonances and discuss how these results inform future EMRI models.