New method to calculate self-force during inspiral into a Kerr black hole

We are developing extreme mass ratio inspiral (EMRI) calculations of the Kerr self-force with methods that avoid time-instabilities encountered in previous work. To develop methods that will be applicable to gravitational perturbations, we examine a toy model consisting of a scalar charge orbiting a Kerr black hole. We will avoid instabilities by separating the "t" variable, and the "phi" variable was separated for simplicity. This leads to elliptic partial differential equations (PDEs) with "r" and "theta" derivatives which are solved via the finite difference method. Preliminary results will be presented to demonstrate progress towards these goals. Our eventual results will enhance theoretical models of gravitational waves detected by the Laser Interferometer Space Antenna (LISA).