Title:

Frequency domain approach to selfforce calculations

In this thesis, the problem of computing the backreaction, or selfforce, caused by a point particle interacting with its own field is studied. In particular, motivated by the prospect of detecting gravitational waves from extreme mass ratio inspiral systems, we consider the motion of the particle in black hole spacetimes. As a toy model for the most astrophysically relevant scenario of orbits about a rotating black hole we first study the scalarfield selfforce (SSF)experienced by a scalar charge moving on a fixed geodesic in Kerr spacetime for a variety of orbits. Our approach is to work in the frequency domain, fully decomposing the scalar field into spheroidal harmonic and frequency modes and numerically solving for the retarded field modebymode. Regularization of the retarded field is performed using the standard modesum technique which requires spherical harmonic modes as input, which we obtain by projecting the spheroidal harmonic modes on to a basis of spherical harmonics. We find for circular, equatorial orbits that the black hole spin can have a pronounced effect on the conservative piece of the SSF, causing it to (with respect to the Schwarzschild scalarfield selfforce) change sign for certain spins and orbital radii. For eccentric orbits in the equatorial plane, we make use of the recently introduced method of extended homogeneous solutions to overcome the Gibbs phenomenon associated with a naive approach. As an application of our work we compute the shift to the innermost stable circular orbit due to the conservative piece of the scalarfield selfforce for a variety of black hole spins. We also present some preliminary results for the SSF along circular, inclined geodesics. As well as studying the toy model SSF, we also consider the gravitational selfforce (GSF) problem in the context of orbits around a Schwarzschild black hole. Our approach is again to work in the frequency domain, and we perform a complete decomposition of the metric perturbation in tensor spherical harmonics and frequency modes. The ten metric perturbation fields decouple with respect to the multipole indices but remain coupled within each spherical harmonic mode. We solve the resulting coupled sets numerically with a code set up to run on a computer cluster. Regularization is again performed using the modesum technique. Our resulting code is extremely efficient for low eccentricity orbits, and using it we compute the GSF for a great many points in the orbital parameter space. With these results we fit an analytic model to our numerical data and then use a relativistic osculating elements scheme to evolve the orbital inspiral. This allows us, for the first time, to assess the contribution to a complete inspiral from the conservative piece of the gravitational selfforce. Finally, as an aside, we investigate the recently discovered phenomenon of isofrequency orbits, whereby it is possible to have pairs of physically distinct bound geodesics about a Kerr black hole that share the same three orbital frequencies.
