arXiv subjects

Donal O'Connell

Publications and source records attributed to Donal O'Connell.

At least 19 recordsLinked to original sources

arXiv2026

Amplitudes for Hawking Radiation

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.

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arXiv2026

Supertranslations are Soft Dressings

Asymptotic states of massive particles in electrodynamics and gravity are not uniquely defined because of the absence of a mass gap. Working in the KMOC formalism, we study the classical implications of this freedom in the dressing of massive particle states. We show that coherent-state dressings modify observables by a large gauge/BMS transformation. The associated coherent-state displacement operator can be completed into a conserved charge, the BMS charge in the gravitational case, which implements large gauge transformations on scattering data. The parameter of our dressing is directly the large gauge/BMS transformation parameter, and we explain that observables do not depend on monopolar and dipolar parts of the transformation parameter to all orders. Our construction is driven by soft factorization rather than by an underlying local symmetry, and we illustrate this by exhibiting the same structure in a scalar theory with no gauge symmetry. We explore the action of large gauge transformations on two-particle states for scalar, abelian gauge and graviton mediators, obtaining a universal shift of the impact parameter and clarifying the frame dependence of the radiated angular momentum vis à vis the frame-independence of the total angular momentum. The transformation connecting the canonical BMS frame, in which the Schwarzschild metric takes the Kerr-Schild form, to the intrinsic frame, in which it takes the De Donder form, illustrates these effects concretely.

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arXiv2026

Type D Spacetimes and the Weyl Double Copy

We study the double-copy relation between classical solutions in gauge theory and gravity, focusing on four-dimensional vacuum metrics of algebraic type D, a class that includes several important solutions. We present a double copy of curvatures that applies to all spacetimes of this type -- the Weyl double copy -- relating the curvature of the spacetime to an electromagnetic field strength. We show that the Weyl double copy is consistent with the previously known Kerr-Schild double copy, and in fact resolves certain ambiguities of the latter. The most interesting new example of the classical double copy presented here is that of the C-metric. This well-known solution, which represents a pair of uniformly accelerated black holes, is mapped to the Lienard-Wiechert potential for a pair of uniformly accelerated charges. We also present a new double-copy interpretation of the Eguchi-Hanson instanton.

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arXiv2026

Hawking Radiation meets the Double Copy

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.

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arXiv2026

The ABCs of Amplitudes, Bogoliubov and Crossing

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.

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arXiv2024

Supertranslations from Scattering Amplitudes

On-shell methods have found a new application to local observables such as asymptotic radiation fields and gravitational waveforms. While these observables are invariant under small gauge transformations, they are known to depend on a choice of asymptotic gauge; in gravity on asymptotically Minkowski spacetimes, this is a choice of BMS frame. In this letter, we provide a method for capturing these supertranslations, to all orders in perturbation theory, using the on-shell framework of scattering amplitudes.

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arXiv2024

Observables from the Spinning Eikonal

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.

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arXiv2024

The Uncertainty Principle and Classical Amplitudes

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 or 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.

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arXiv2024

Radiation and Reaction at One Loop

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. We show that the real and imaginary parts of the amplitudes both play important but physically distinct roles in the radiation field. The amplitude's imaginary part directly computes the portion of radiation emitted under the influence of a body's self-field, i.e., through radiation reaction. This aspect of radiation reaction is directly linked to one-loop Compton amplitudes in electrodynamics, Yang-Mills theory and gravity. We also discuss the fascinating interplay between renormalisation, radiation reaction and classical field theory from this perspective.

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arXiv2023

The SAGEX Review on Scattering Amplitudes

This is an introduction to, and invitation to read, a series of review articles on scattering amplitudes in gauge theory, gravity, and superstring theory. Our aim is to provide an overview of the field, from basic aspects to a selection of current (2022) research and developments.

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arXiv2022

Large Gauge Effects and the Structure of Amplitudes

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.

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arXiv2022

NS-NS Spacetimes from Amplitudes

Recent work has shown how on-shell three-point amplitudes in gauge theory and gravity, representing the coupling to massive particles, correspond in the classical limit to the curvature spinors of linearised solutions. This connection, made explicit via the KMOC formalism in split metric signature, turns the double copy of scattering amplitudes into the double copy of classical solutions. Here, we extend this framework to the universal massless sector of supergravity, which is the complete double copy of pure gauge theory. Our extension relies on a Riemann-Cartan curvature incorporating the dilaton and the B-field. In this setting, we can determine the most general double copy arising from the product of distinct gauge theory solutions, say a dyon and $\sqrt{\text{Kerr}}$. This gives a double-copy interpretation to gravity solutions of the type Kerr-Taub-NUT-dilaton-axion. We also discuss the extension to heterotic gravity. Finally, we describe how this formalism for the classical double copy relates to others in the literature, namely (i) why it is an on-shell momentum space analogue of the convolutional prescription, and (ii) why a straightforward prescription in position space is possible for certain vacuum solutions.

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arXiv2022

The SAGEX Review on Scattering Amplitudes, Chapter 14: Classical Gravity from Scattering Amplitudes

Scattering amplitudes have their origin in quantum field theory, but have wide-ranging applications extending to classical physics. We review a formalism to connect certain classical observables to scattering amplitudes. An advantage of this formalism is that it enables us to study implications of the double copy in classical gravity. We discuss examples of observables including the total change of a particle's momentum, and the gravitational waveform, during a scattering encounter. The double copy also allows direct access to classical solutions in gravity. We review this classical double copy starting from its linearised level, where it originates in the double copy of three-point amplitudes. The classical double copy extends elegantly to exact solutions, making a connection between scattering amplitudes and the geometric formulation of General Relativity.

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arXiv2022

Snowmass White Paper: the Double Copy and its Applications

The double copy is, in essence, a map between scattering amplitudes in a broad variety of familiar field and string theories. In addition to the mathematically rich intrinsic structure, it underlies a multitude of active research directions and has a range of interesting applications in quantum, classical and effective field theories, including broad topics such as string theory, particle physics, astrophysics, and cosmology. This Snowmass white paper provides a brief introduction to the double copy, its applications, current research and future challenges.

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arXiv2022

Snowmass White Paper: Gravitational Waves and Scattering Amplitudes

We review recent progress and future prospects for harnessing powerful tools from theoretical high-energy physics, such as scattering amplitudes and effective field theory, to develop a precise and systematically improvable framework for calculating gravitational-wave signals from binary systems composed of black holes and/or neutron stars. This effort aims to provide state-of-the-art predictions that will enable high-precision measurements at future gravitational-wave detectors. In turn, applying the tools of quantum field theory in this new arena will uncover theoretical structures that can transform our understanding of basic phenomena and lead to new tools that will further the cycle of innovation. While still in a nascent stage, this research direction has already derived new analytic results in general relativity, and promises to advance the development of highly accurate waveform models for ever more sensitive detectors.

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arXiv2021

Waveforms from Amplitudes

We show how to compute classical wave observables using quantum scattering amplitudes. We discuss observables both with incoming and with outgoing waves. The required classical limits are naturally described by coherent states of massless bosons. We recompute the classic gravitational deflection of light, and also show how to rederive Thomson scattering. We introduce a new class of local observables, which includes the asymptotic electromagnetic and gravitational Newman--Penrose scalars. As an example, we compute a simple radiated waveform: the expectation of the electromagnetic field in charged-particle scattering. At leading order, the waveform is trivially related to the five-point scattering amplitude.

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arXiv2021

A worldsheet for Kerr

We show that the Newman-Janis shift property of the exact Kerr solution can be interpreted in terms of a worldsheet effective action. This holds both in gravity, and for the single-copy $\sqrt{\text{Kerr}}$ solution in electrodynamics. At the level of equations of motion, we show that the Newman-Janis shift holds also for the leading interactions of the Kerr black hole. These leading interactions are conveniently described using chiral classical equations of motion with the help of the spinor-helicity method familiar from scattering amplitudes.

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arXiv2020

Classical Solutions and their Double Copy in Split Signature

The three-point amplitude is the key building block in the on-shell approach to scattering amplitudes. We show that the classical objects computed by massive three-point amplitudes in gauge theory and gravity are Newman-Penrose scalars in a split-signature spacetime, where three-point amplitudes can be defined for real kinematics. In fact, the quantum state set up by the particle is a coherent state fully determined by the three-point amplitude due to an eikonal-type exponentiation. Having identified this simplest classical solution from the perspective of scattering amplitudes, we explore the double copy of the Newman-Penrose scalars induced by the traditional double copy of amplitudes, and find that it coincides with the Weyl version of the classical double copy. We also exploit the Kerr-Schild version of the classical double copy to determine the exact spacetime metric in the gravitational case. Finally, we discuss the direct implication of these results for Lorentzian signature via analytic continuation.

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