The On-Shell Highway To Waveforms

Andrea Cristofoli

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Abstract

This thesis explores several dynamical aspects of the classical two-body problem using scattering amplitude methods. We first discuss the conservative two-body dynamics in General Relativity in the post-Minkowskian regime, valid for weak gravitational fields and unbound velocities. In doing so, we present novel rela- tions between on-shell scattering amplitudes and classical quantities such as the post-Minkowskian Hamiltonian and scattering angle. We then focus on modern am- plitude methods, presenting the string inspired CHY formalism. As an application, we derive covariant expressions for tree-level amplitudes with two massive scalars and an arbitrary number of gravitons, providing the needed input to evaluate classical observables from unitarity methods. We then study classical wave physics, showing how to derive from amplitudes gravitational shock wave solutions to Einstein field equations. We conclude by presenting a generalization of a formalism developed by David Kosower, Ben Maybee and Donal O’Connell, which describes black hole dynamics from on-shell data. With the addition of coherent states in the original framework, we study observables with massless particles as incoming states, such as the bending of light and the Thomson scattering. We also derive waveforms generated in binary scattering, providing an elegant relation between the Newman-Penrose formalism and helicity amplitudes.

Funded in part by the European Union’s Horizon 2020 Framework Program under the Marie Skłodowska-Curie grant agreement No. 764850 (SAGEX).