Donal O'Connell

A bstract: It is now common to describe classical backgrounds involving dynamical black holes with the production of gravitational radiation using the methods of scattering amplitudes. In that light, we revisit the standard formulation of quantum field theory on a background. We discuss the interpretation of Bogoliubov coefficients as generalised amplitudes, and explain how crossing, analyticity, and causality relate the relevant set of amplitudes. When the background is itself a coherent state, we map these statements onto standard results in flat-space quantum field theory.

A bstract: We obtain the Hawking spectrum by exponentiating a series of Feynman diagrams describing a scalar field scattering through a collapse background. Our approach is rooted in semiclassical methods of scattering amplitudes which have recently been developed for application to gravitational-wave physics. The diagrams we encounter do not compute a standard amplitude, but rather an in-in generalisation of an amplitude which is closely connected to the Bogoliubov coefficients. We also compute the subdominant one-loop correction in our perturbative approach, analogous to the triangle correction to Schwarzschild scattering. This term can be interpreted as a finite-size correction sensitive to the radius of the black hole.

A bstract: We describe an electromagnetic system which is related to black hole production with Hawking radiation through the double copy. We consider the scattering of a massless scalar particle through a collapsing electromagnetic background — the single copy of Vaidya — and identify the Feynman diagrams that exponentiate in the geometric-optics limit. The Bogoliubov coefficients obtained from the diagrammatic approach are reproduced by a semiclassical ray-tracing computation of null rays in this same background. We discuss the thermodynamic interpretation of the resulting number distribution in light of the double copy.

We obtain the Hawking spectrum by exponentiating a series of Feynman diagrams describing a scalar field scattering through a collapse background. Our approach is rooted in semiclassical methods of scattering amplitudes which have recently been developed for application to gravitational-wave physics. The diagrams we encounter do not compute a standard amplitude, but rather an in-in generalisation of an amplitude which is closely connected to the Bogoliubov coefficients. We also compute the subdominant one-loop correction in our perturbative approach, analogous to the triangle correction to Schwarzschild scattering. This term can be interpreted as a finite-size correction sensitive to the radius of the black hole.

We study the classical dynamics of spinning particles using scattering amplitudes and eikonal exponentiation. We show that observables are determined by a simple algorithm. A wealth of complexity arises in perturbation theory as positions, momenta and spins must be iteratively corrected at each order. Even though we restrict ourselves to one-loop computations at quadratic order in spin, nevertheless we encounter and resolve a number of subtle effects. Finally, we clarify the links between our work and various other eikonal approaches to spinning observables.

We study classical radiation fields at next-to-leading order using the methods of scattering amplitudes. The fields of interest to us are sourced when two massive, point-like objects scatter inelastically, and can be computed from one-loop amplitudes. The real and imaginary parts of the amplitudes play important but physically distinct roles in the radiation field. We argue that the imaginary part captures the effects of radiation reaction. This aspect of radiation reaction is directly linked to cuts of one-loop amplitudes which expose Compton trees. We also discuss the fascinating interplay between renormalisation, radiation reaction and classical field theory from this perspective.

We study the variance in the measurement of observables during scattering events, as computed using amplitudes. The classical regime, characterised by negligible uncertainty, emerges as a consequence of an infinite set of relationships among multileg, multiloop amplitudes in a momentum-transfer expansion. We discuss two non-trivial examples in detail: the six-point tree and the five-point one-loop amplitudes in scalar QED. We interpret these relationships in terms of a coherent exponentiation of radiative effects in the classical limit which generalises the eikonal formula, and show how to recover the impulse, including radiation reaction, from this generalised eikonal. Finally, we incorporate the physics of spin into our framework.

We extract the relativistic classical radial action from scattering amplitudes, to all orders in perturbation theory, in the probe limit. Our sources include point charges and monopoles, as well as the Schwarzschild and pure-NUT gravitational backgrounds. A characteristic relativistic effect, that scattering trajectories may wind around these sources any number of times, can be recovered when all-order amplitudes are available. We show that the amplitude for scattering a probe off a pure NUT is given by the solution of a transcendental equation involving continued fractions, and explain how to solve this equation to any desired loop order.

We show that large gauge transformations modify the structure of momentum conservation leading to non-vanishing three-point amplitudes in a simple toy model of a gravitational wave event. This phenomenon resolves an apparent tension between perturbative scattering amplitude computations and exact methods in field theory. The tension is resolved to all orders of perturbation theory once large gauge effects are included via a modified LSZ prescription; if they are omitted, perturbative methods only recover a subset of terms in the full non-perturbative expression. Although our results are derived in the context of specific examples, several aspects of our work have analogues in dynamical gravitational scattering processes.

We show that large gauge transformations modify the structure of momentum conservation leading to non-vanishing three-point amplitudes in a simple toy model of a gravitational wave event. This phenomenon resolves an apparent tension between perturbative scattering amplitude computations and exact methods in field theory. The tension is resolved to all orders of perturbation theory once large gauge effects are included via a modified LSZ prescription; if they are omitted, perturbative methods only recover a subset of terms in the full non-perturbative expression. Although our results are derived in the context of specific examples, several aspects of our work have analogues in dynamical gravitational scattering processes.