Scattering waveforms for Kerr black holes from the soft expansion

TL;DR

This thesis develops a novel approach combining quantum field theory techniques and soft theorems to analyze gravitational scattering of spinning Kerr black holes, deriving waveforms and amplitudes in the Post-Minkowskian expansion.

Contribution

It generalizes the subleading soft theorem to spinning particles and computes gravitational waveforms for Kerr black hole scattering at leading PM order.

Findings

Derived the gravitational Compton amplitude for spinning particles.

Computed the tree-level five-point amplitude with graviton emission.

Produced the analytic time-domain waveform for Kerr black hole scattering.

Abstract

In this thesis, I will study the classical scattering problem of two Kerr black holes in general relativity with novel quantum field theory techniques in the Post-Minkowskian (PM) expansion, generalizing the subleading soft theorem to the case of spinning particles. The leading order term in the soft expansion is uniquely determined by the universal Weinberg pole, but the subleading one depends on the angular momentum of the external particles and receives a new spin corrections for classically spinning black holes. Using this approach, I will compute the gravitational Compton amplitude, both in the quantum and classical theory. I will then compute the tree-level five-point amplitude of two spinning point particles emitting a graviton, using the spinor-helicity formalism combined with the soft expansion. Finally, I will use the KMOC formalism to derive the analytic time-domain waveform for the scattering of two Kerr black holes at leading order in the PM expansion.