Abstract:
Black hole perturbation theory is the main tool used for self-force calculations and relies on a small mass ratio to yield perturbatively small corrections off of background geodesic motion. For extreme mass ratio inspirals (EMRIs), the mass ratio is typically smaller than 1/100,000, but a mass ratio of 1/10 is also small and one may try to push perturbation theory to less extreme mass ratios. I discuss ongoing work in this direction within the context of a nonlinear scalar model that serves as a strong analog of the gravitational EMRI problem. For quasi-circular inspirals, this model can be resummed exactly in the mass ratio to yield non-perturbative expressions for the conservative self-force, ISCO shift, energy, etc. Having exact expressions for these quantities then allows one to compare with the perturbative expressions and estimate the errors made as the mass ratio becomes less extreme. I also discuss a simple way to improve first-order accurate expressions that carries over directly to gravitational EMRIs. This could provide a complementary way to study black hole binaries with comparable masses using self-force techniques. |