Eccentric self-forced inspirals into a rotating black hole

TL;DR

This paper introduces a fast, accurate model for extreme mass-ratio inspirals into rotating black holes driven by gravitational self-force, enabling efficient waveform generation for gravitational wave detection.

Contribution

It develops the first self-force based inspiral model using an action-angle approach and spectral interpolation, allowing rapid evolution without resolving all orbital cycles.

Findings

Model can be evaluated in less than a second for any mass ratio.

Self-force data in different gauges produce comparable but distinct inspirals.

Including second order self-force is necessary for gauge-independent waveforms.

Abstract

We develop the first model for extreme mass-ratio inspirals (EMRIs) into a rotating massive black hole driven by the gravitational self-force. Our model is based on an action angle formulation of the method of osculating geodesics for eccentric, equatorial (i.e., spin-aligned) motion in Kerr spacetime. The forcing terms are provided by an efficient spectral interpolation of the first-order gravitational self-force in the outgoing radiation gauge. We apply a near-identity (averaging) transformation to eliminate all dependence of the orbital phases from the equations of motion, while maintaining all secular effects of the first-order gravitational self-force at post-adiabatic order. This implies that the model can be evolved without having to resolve all $\mathcal{O}(10^5)$ orbit cycles of an EMRI, yielding an inspiral model that can be evaluated in less than a second for any mass-ratio. In the case of a non-rotating central black hole, we compare inspirals evolved using self-force data computed in the Lorenz and radiation gauges. We find that the two gauges generally produce differing inspirals with a deviation of comparable magnitude to the conservative self-force correction. This emphasizes the need for including the (currently unknown) dissipative second order self-force to obtain gauge independent, post-adiabatic waveforms.