UCLA

Amplitudes methods have found increasingly varied applications across physics, in particular in the field of gravitational waves. In this manuscript we will present how amplitudes techniques apply to interactions of gravitating spinning bodies. We will analyze the amplitudes of generic spinning bodies and pay special attention to how the structure of these amplitudes simplifies when specializing to spinning black holes. In Chapter 1, we develop how several amplitudes tools such as the Kosower-Maybee-O'Connell formalism, eikonal methods, and effective field theory in the classical limit apply to the dynamics of classically colored particles. Classically colored particles share many of the theoretical features of classical spinning bodies, with the color directly analogous to the spin in many ways, and so serve as an effective proof of concept of how these same tools may be applied to spinning bodies. In Chapter 2, we directly apply these techniques to classical spinning electromagnetically interacting bodies, which share all of the spin related complications of the gravitational problem while being simpler due to the relative simplicity of electromagnetism compared to gravity. In doing so, we find that the effective field theory is capable of carrying an extra vector degree of freedom compared with the previously established worldline formalism, and that that vector degree of freedom allows for spin magnitude change in the theory. We also present a modification of the traditional worldline formalism which perfectly matches the effective field theory. In Chapter 3, we use the worldline formalism to compute generic spinning body Compton amplitudes through the fifth order in spin, at which several interesting complications occur. This Compton amplitude is essential for computing one-loop observables for the spinning binary system. We then use Dixon's multipole moment formalism to identify an effective source energy-momentum tensor for a spinning black hole, which if treated as appropriate in the effective theory determines several previously unconstrained Wilson coefficients which affect black hole observables. In Chapter 4, we extend the electromagnetic methods of Chapter 2 to gravity. We find that the nonminimal degrees of freedom persist in having matching physical effects between the worldline and field theory approaches. As well, we find that those degrees of freedom have observable effects on the gravitational waveform.