Computing gravitational perturbations and metric reconstruction for extreme-mass-ratio inspirals on a Schwarzschild black hole using frequency domain methods

Extreme-mass-ratio binaries, composed of a small compact object (SCO) and supermassive black hole (SMBH), are eventual observational candidates for future space-based gravitational wave observatories.  Theoretically, these binaries are examples of the as-yet not thoroughly solved two-body problem in general relativity.  Extreme-mass-ratio inspiral (EMRI) calculations proceed by using black hole perturbation theory.  The gravitational field of the small mass affects its own orbit in the background geometry, leading to a radiation reaction that is formally divergent.  Regularization procedures tell how to compute the finite corrections to the SCOs orbit (the self force).  These require accurate knowledge of the perturbed metric.  We describe two, similar methods for computing the first-order gravitational perturbations and accurately determining the local perturbations in the metric.  Both involve use of mixed frequency domain/time domain methods.