Self-Force on Accelerated Particles

Abstract

The likelihood that gravitational waves from stellar-size black holes spiraling into a supermassive black hole would be detectable by a space based gravitational wave observatory has spurred the interest in studying the extreme mass-ratio inspiral (EMRI) problem and black hole perturbation theory (BHP). In this approach, the smaller black hole is treated as a point particle and its trajectory deviates from a geodesic due to the interaction with its own field. This interaction is known as the gravitational self-force, and it includes both a damping force, commonly known as radiation reaction, as well as a conservative force. The computation of this force is complicated by the fact that the formal expression for the force due to a point particle diverges, requiring a careful regularization to find the finite self-force. This dissertation focuses on the computation of the scalar, electromagnetic and gravitational self-force on accelerated particles. We begin with a discussion of the "MiSaTaQuWa" prescription for self-force renormalization (Mino, Sasaki, Takasugi 1999 and Quinn and Wald, 1999) along with the refinements made by Detweiler and Whiting (2003), and demonstrate how this prescription is equivalent to performing an angle average and renormalizing the mass of the particle. With this background, we shift to a discussion of the ``mode-sum renormalization" technique developed by Barack and Ori (2000), who demonstrated that for particles moving along a geodesic in Schwarzschild spacetime (and later in Kerr spacetime), the regularization parameters can be described using only the leading and subleading terms (known as the A and B terms). We extend this to demonstrate that this is true for fields of spins 0, 1, and 2, for accelerated trajectories in arbitrary spacetimes. Using these results, we discuss the renormalization of a charged point mass moving through an electrovac spacetime; extending previous studies to situations in which the gravitational and electromagnetic contributions are comparable. We renormalize by using the angle average plus mass renormalization in order to find the contribution from the coupling of the fields and encounter a striking result: Due to a remarkable cancellation, the coupling of the fields does not contribute to the renormalization. This means that the renormalized mass is obtained by subtracting (1) the purely electromagnetic contribution from a point charge moving along an accelerated trajectory and (2) the purely gravitational contribution of an electrically neutral point mass moving along the same trajectory. In terms of the mode-sum regularization, the same cancellation implies that the regularization parameters are merely the sums of their purely electromagnetic and gravitational values. Finally, we consider the scalar self-force on a point charge orbiting a Schwarzschild black-hole following a non-Keplerian circular orbit. We utilize the techniques of Mano, Suzuki, and Takasugi (1996) for generating analytic solutions. With this tool, it is possible to generate a solution for the field as a series in the Fourier frequency, which allows researchers to naturally express the solutions in a post Newtonian series (see Shah et. al. 2014). We make use of a powerful insight by Hikida et. al.(2005), which allows us to perform the renormalization analytically. We investigate the details of this procedure and illuminate the mechanisms through which it works. We finish by demonstrating the power of this technique, showing how it is possible to obtain the post Newtonian expressions by only explicitly computing a handful of modes.