Gravitational Wave Modeling of Extreme Mass Ratio Inspirals Perturbed by an Outer Supermassive Black Hole

We apply the method of osculating orbits in the Schwarzschild–Droste space-time using the relativistic orbital evolution equations for a perturbed extreme mass ratio inspiral (EMRI) by an outer supermassive black hole. The latter supposedly lies in the orbital plane, so that the orbital elements related to inclination and ascending node do not play a role. Our approach encompasses both strong and weak gravity fields. For calculating the gravitational waveforms of perturbed EMRIs through the Regge–Wheeler–Zerilli wave equations, we apply the second-order source-free integration method. Designed for integration in the time domain, our algorithm consists of a finite difference scheme that discretizes the space-time into a grid cell \((t,r^{*})\), whereas the discontinuity of the gravity field at the world line of the particle is dealt with jump conditions on the wave function and its derivatives.