Self-force on a scalar charge in Kerr spacetime: Eccentric equatorial orbits

Abstract

We present a numerical code for calculating the self force on a scalar charge moving in a bound (eccentric) geodesic in the equatorial plane of a Kerr black hole. We work in the frequency domain and make use of the method of extended homogeneous solutions [Phys.\ Rev.\ D {\bf 78}, 084021 (2008)], in conjunction with mode-sum regularization. Our work is part of a program to develop a computational architecture for fast and efficient self-force calculations, alternative to time-domain methods. We find that our frequency-domain method outperforms existing time-domain schemes for small eccentricities, and, remarkably, remains competitive up to eccentricities as high as $\sim 0.7$. As an application of our code we (i) compute the conservative scalar-field self-force correction to the innermost stable circular equatorial orbit, as a function of the Kerr spin parameter; and (ii) calculate the variation in the rest mass of the scalar particle along the orbit, caused by the component of the self force tangent to the four-velocity.