arXiv subjects

Tim Adamo

Publications and source records attributed to Tim Adamo.

At least 19 recordsLinked to original sources

arXiv2026

Schwarzschild black holes from twistor space

Twistor theory forms the basis for many surprising advances in areas ranging from dynamical systems to quantum field theory. Yet for almost fifty years, one of the main drawbacks of twistor theory has been its inability to give non-perturbative descriptions of non-chiral (or non-self-dual) field configurations. This difficulty is known as 'the googly problem.' In this paper, we provide a resolution of the googly problem for a particular solution of the vacuum Einstein equations: the Schwarzschild metric. We start with the twistor space of the self-dual Taub-NUT Euclidean gravitational instanton, expressed in Kerr-Schild form. Within this twistor space, we then consider a quadric which corresponds to the anti-self-dual Taub-NUT metric. While the full quadric is not holomorphic with respect to the complex structure of the self-dual Taub-NUT twistor space, its holomorphic locus still has complex dimension two. This 'coincidence locus' -- points in twistor space on the holomorphic portion of the quadric -- inherits a complex structure from the twistor space and a K\"ahler form from the quadric itself. Remarkably, these structures are compatible, giving rise to a non-self-dual, four-dimensional K\"ahler metric which is conformal to Schwarzschild (in Lorentzian or Euclidean signature). This is the first instance of a non-self-dual Einstein metric constructed entirely from holomorphic data in a twistor space.

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arXiv2026

Scattering and depletion in a flying focus from conformal transformations

We show that flying focus fields can be obtained from complex conformal transformation of plane waves, and that solutions of the massless wave equation in the so-obtained fields are, correspondingly, conformal transformations of the Volkov solutions. This leads to the result that photon emission amplitudes in a totally depleting flying focus beam may be computed directly from the corresponding plane wave amplitudes by taking a simple Gaussian average over certain momentum variables. In effect, this gives a way of introducing focussing effects into strong-field QED calculations `for free'. The extension of these results to scattering amplitudes including only partial depletion is discussed and some first results presented in the anti-self-dual limit.

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arXiv2026

The dual twistor theory of self-dual black holes

The Taub-NUT and Eguchi-Hanson gravitational instantons, along with the self-dual Plebanski-Demianski metric, form a set of Euclidean metrics which can naturally be called `self-dual black holes', as they arise from self-dual slices of the most general vacuum, asymptotically flat black hole metric. These self-dual black holes are of interest for many reasons, and can famously be described through the non-linear graviton construction of twistor theory. However, the implicit nature of this twistor description obscures some features of the underlying geometry, particularly for the most general self-dual black holes. In this paper, we give a new construction of all asymptotically flat self-dual black holes based on holomorphic quadrics in flat dual twistor space, rather than the usual twistor space associated with self-duality. Remarkably, the geometry of the self-dual black holes -- including their hyperkahler structure, as well as Kerr-Schild and Gibbons-Hawking forms -- is directly encoded in the corresponding quadric. As a consequence, we obtain a previously unknown single Kerr-Schild form of the self-dual Plebanski-Demianski metric.

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arXiv2025

From AdS correlators to Carrollian amplitudes with the scattering equation

The scattering equations relate massless scattering kinematics to marked points on a Riemann sphere, and underpin remarkable formulae for the full tree-level S-matrices of many interesting QFTs, including cubic biadjoint scalars, Yang-Mills theory and general relativity. The scattering equations arise from worldsheet correlators of ambitwistor string theories, which has enabled their generalisation to anti-de Sitter (AdS) space in certain cases. In this paper, we use the scattering equations and ambitwistor strings to prove the correspondence between an appropriate flat limit of boundary correlators in AdS and Carrollian scattering amplitudes -- massless amplitudes written in position space on the null conformal boundary -- for any number of external states and spacetime dimensions in tree-level, cubic scalar theories. We first derive the Carrollian version of the scattering equations in Minkowski space and their associated Carrollian amplitude formulae, by direct Fourier transform from momentum space and from ambitwistor strings with a Carrollian basis of vertex operators. We then take the flat limit of known formulae for all tree-level boundary correlators of cubic scalar theories in AdS, recovering the Carrollian amplitudes in flat space. In the special case of AdS$_3$, we also make some comments on the flat space limit of spinning boundary correlators.

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arXiv2025

Graviton scattering on self-dual black holes

The computation of gravitational wave scattering on black hole spacetimes is an extremely hard problem, typically requiring approximation schemes that either treat the black hole perturbatively or are only amenable to numerical techniques. In this paper, we consider linearised gravitational waves (or gravitons) scattering on the self-dual analogue of a black hole: namely, the self-dual Taub-NUT metric. Using the hidden integrability of the self-dual sector, we solve the linearised Einstein equations on these self-dual black hole backgrounds exactly in terms of simple, explicit quasi-momentum eigenstates. Using a description of the self-dual Taub-NUT metric and its gravitons in terms of twistor theory, we obtain an explicit formula, exact in the background, for the tree-level maximal helicity violating (MHV) graviton scattering amplitude at arbitrary multiplicity, with and without spin. This is obtained from the description of the MHV amplitudes in terms of the perturbation theory of a chiral sigma model whose target is the twistor space of the background. The incorporation of spin effects on these backgrounds is a straightforward application of the Newman-Janis shift. We also demonstrate that the holomorphic collinear splitting functions in the self-dual background are equal to those in flat space so that the celestial symmetry algebra is undeformed.

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arXiv2025

Twistorial chiral algebras in higher dimensions

In four spacetime dimensions, the classically integrable self-dual sectors of gauge theory and gravity have associated chiral algebras, which emerge naturally from their description in twistor space. We show that there are similar chiral algebras associated to integrable sectors of gauge theory and gravity whenever the spacetime dimension is an integer multiple of four. In particular, the hyperk\"ahler sector of gravity and the hyperholomorphic sector of gauge theory in $4m$-dimensions have well-known twistor descriptions giving rise to chiral algebras. Using twistor sigma models to describe these sectors, we demonstrate that the chiral algebras in higher-dimensions also arise as soft symmetry algebras under a certain notion of collinear limit. Interestingly, the chiral algebras and collinear limits in higher-dimensions are defined on the 2-sphere, rather than the full celestial sphere.

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arXiv2025

Scattering with total depletion in strong, focussed fields

Theoretical approaches to QED scattering in strong fields typically treat the field as a fixed background with simple spacetime dependence, such as a plane wave. Two major challenges are therefore the inclusion of backreaction (e.g. depletion of the field) and spatial geometry (e.g. focussing). We show here that a solution to one problem can solve the other: even if particle wavefunctions in a chosen focussed background are not known, we show they can be constructed once depletion is accounted for. We demonstrate this by giving the exact wavefunctions in a flying focus beam for which all energy is absorbed by particles scattering on it. In addition we use the wavefunctions to obtain a simple expression for the nonlinear Compton scattering amplitude, comparing with the plane wave case. Our methods thus open a new avenue of investigation in which two previously challenging effects are simultaneously brought under analytic control.

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arXiv2024

Gluon scattering on the self-dual dyon

The computation of scattering amplitudes in the presence of non-trivial background gauge fields is an important but extremely difficult problem in quantum field theory. In even the simplest backgrounds, obtaining explicit formulae for processes involving more than a few external particles is often intractable. Recently, it has been shown that remarkable progress can be made by considering background fields which are chiral in nature. In this paper, we obtain a compact expression for the tree-level, maximal helicity violating (MHV) scattering amplitude of an arbitrary number of gluons in the background of a self-dual dyon. This is a Cartan-valued, complex gauge field sourced by a point particle with equal electric and magnetic charges, and can be viewed as the self-dual version of a Coulomb field. Twistor theory enables us to manifest the underlying integrability of the self-dual dyon, trivializing the perturbative expansion in the MHV sector. The formula contains a single position-space integral over a spatial slice, which can be evaluated explicitly in simple cases. As an application of the formula, we show that the holomorphic collinear splitting functions of gluons in the self-dual dyon background are un-deformed from a trivial background, meaning that holomorphic celestial OPE coefficients and the associated chiral algebra are similarly un-deformed. We also comment on extensions of our MHV formula to the full tree-level gluon S-matrix.

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arXiv2024

The KLT kernel in twistor space

The double copy relationship between Yang-Mills theory and general relativity can be stated in terms of a field theory Kawai-Lewellen-Tye (KLT) momentum kernel, which maps two colour-ordered gluon amplitudes to a graviton amplitude at tree-level. These amplitudes can also be written in compact, helicity-graded representations on twistor space which include the famous Parke-Taylor and Hodges formulae in the maximal helicity violating sector. However, a double copy formulation of these helicity-graded formulae has proved elusive. In this paper, we use graph-theoretic methods to obtain an explicit double copy representation of the tree-level, helicity graded S-matrix of general relativity in terms of a KLT-like integral kernel in twistor space. This integral kernel glues together two colour-ordered integrands for tree-level gluon scattering on twistor space to produce tree-level graviton amplitudes, and admits a chiral splitting into positive and negative helicity degrees of freedom. Furthermore, the kernel can be inverted to obtain a new formula for the tree-level S-matrix of biadjoint scalar theory, which we verify using recursion relations. We also derive extensions of this integral kernel to graviton scattering in anti-de Sitter space and self-dual radiative spacetimes, commenting on their potential double copy interpretations.

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arXiv2024

Eikonal amplitudes on the celestial sphere

Celestial scattering amplitudes for massless particles are Mellin transforms of momentum-space scattering amplitudes with respect to the energies of the external particles, and behave as conformal correlators on the celestial sphere. However, there are few explicit cases of well-defined celestial amplitudes, particularly for gravitational theories: the mixing between low- and high-energy scales induced by the Mellin transform generically yields divergent integrals. In this paper, we argue that the most natural object to consider is the gravitational amplitude dressed by an oscillating phase arising from semi-classical effects known as eikonal exponentiation. This leads to gravitational celestial amplitudes which are analytic, apart from a set of poles at integer negative conformal dimensions, whose degree and residues we characterize. We also study the large conformal dimension limits, and provide an asymptotic series representation for these celestial eikonal amplitudes. Our investigation covers two different frameworks, related by eikonal exponentiation: $2\to2$ scattering of scalars in flat spacetime and $1\to1$ scattering of a probe scalar particle in a curved, stationary spacetime. These provide data which any putative celestial dual for Minkowski, shockwave or black hole spacetimes must reproduce. We also derive dispersion and monodromy relations for these celestial amplitudes and discuss Carrollian eikonal-probe amplitudes in curved spacetimes.

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arXiv2024

Gravitational Bound Waveforms from Amplitudes

With the aim of computing bound waveforms from scattering amplitudes, we explore gravitational two-body dynamics using the Schwinger-Dyson equations and Bethe-Salpeter recursion. We show that the tree-level scattering waveform admits a natural analytic continuation, in rapidity, to the bound waveform, which we confirm from an independent calculation, in the Post-Newtonian expansion, of the time-domain multipoles at large eccentricity. We demonstrate consistency of this scattering-to-bound map with the Damour-Deruelle prescription for orbital elements in the quasi-Keplerian parametrization (which enters into the evaluation of the multipoles) and with the analytic continuation, in the binding energy, of radiated energy and angular momentum at 3PM.

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arXiv2023

Scattering on self-dual Taub-NUT

We derive exact solutions of massless free field equations and tree-level two-point amplitudes up to spin 2 on self-dual Taub-NUT space-time, as well as on its single copy, the self-dual dyon. We use Killing spinors to build analogues of momentum eigenstates, finding that, in the spirit of color-kinematics duality, those for the self-dual dyon lift directly to provide states on the self-dual Taub-NUT background if one replaces charge with energy. We discover that they are forced to have faster growth at infinity than in flat space due to the topological non-triviality of these backgrounds. The amplitudes for massless scalars and spinning particles in the $(+\,+)$ and $(+\,-)$ helicity configurations vanish for generic kinematics as a consequence of the integrability of the self-dual sector. The $(-\,-)$ amplitudes are non-vanishing and we compute them exactly in the backgrounds, which are treated non-perturbatively. It is explained how spin is easily introduced via a Newman-Janis imaginary shift along the spin-vector leading directly to the additional well-known exponential factor in the dot product of the spin with the momenta. We also observe a double copy relation between the gluon amplitude on a self-dual dyon and graviton amplitude on a self-dual Taub-NUT space-time.

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arXiv2023

Infrared structures of scattering on self-dual radiative backgrounds

The scattering of gluons and gravitons in trivial backgrounds is endowed with many surprising infrared features which have interesting conformal interpretations on the two-dimensional celestial sphere. However, the fate of these structures in more general asymptotically flat backgrounds is far from clear. In this paper, we consider holomorphic infrared structures in the presence of non-perturbative, self-dual background gauge and gravitational fields which are determined by freely specified radiative data. We make use of explicit formulae for tree-level gluon and graviton scattering in these self-dual radiative backgrounds, as well as chiral twistor sigma model descriptions of the classical dynamics. Remarkably, we find that the leading holomorphic part of tree-level collinear splitting functions -- or celestial OPEs -- and infinite-dimensional chiral soft algebras are undeformed by the background. We also compute all-order holomorphic celestial OPEs in the MHV sectors of gauge theory and gravity.

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arXiv2023

Scattering amplitudes for self-force

The self-force expansion allows the study of deviations from geodesic motion due to the emission of radiation and its consequent back-reaction. We investigate this scheme within the on-shell framework of semiclassical scattering amplitudes for particles emitting photons or gravitons on a static, spherically symmetric background. We first present the exact scalar 2-point amplitudes for Coulomb and Schwarzschild, from which one can extract classical observables such as the change in momentum due to geodesic motion. We then present, for the first time, the 3-point semiclassical amplitudes for a scalar emitting a photon in Coulomb and a graviton on linearised Schwarzschild, outlining how the latter calculation can be generalized to the fully non-linear Schwarzschild metric. Our results are proper resummations of perturbative amplitudes in vacuum but, notably, are expressed in terms of Hamilton's principal function for the backgrounds, rather than the radial action.

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arXiv2022

Bethe-Salpeter equation for classical gravitational bound states

The Bethe-Salpeter equation is a non-perturbative, relativistic and covariant description of two-body bound states. We derive the classical Bethe-Salpeter equation for two massive point particles (with or without spin) in a bound gravitational system. This is a recursion relation which involves two-massive-particle-irreducible diagrams in the space of classical amplitudes, defined by quotienting out by symmetrization over internal graviton exchanges. In this context, we observe that the leading eikonal approximation to two-body scattering arises directly from unitarity techniques with a coherent state of virtual gravitons. More generally, we solve the classical Bethe-Salpeter equation analytically at all orders by exponentiating the classical kernel in impact parameter space. We clarify the connection between this classical kernel and the Hamilton-Jacobi action, making manifest the analytic continuation between classical bound and scattering observables. Using explicit analytic resummations of classical (spinless and spinning) amplitudes in momentum space, we further explore the relation between poles with bound state energies and residues with bound state wavefunctions. Finally, we discuss a relativistic analogue of Sommerfeld enhancement which occurs for bound state cross sections.

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arXiv2022

All-order celestial OPE in the MHV sector

On-shell kinematics for gluon scattering can be parametrized with points on the celestial sphere; in the limit where these points collide, it is known that tree-level gluon scattering amplitudes exhibit an operator product expansion (OPE)-like structure. While it is possible to obtain singular contributions to this celestial OPE, getting regular contributions from both holomorphic and anti-holomorphic sectors is more difficult. In this paper, we use twistor string theory to describe the maximal helicity violating (MHV) sector of tree-level, four-dimensional gluon scattering as an effective 2d conformal field theory on the celestial sphere. By organizing the OPE between vertex operators in this theory in terms of soft gluon descendants, we obtain all-order expressions for the celestial OPE which include all regular contributions in the collinear expansion. This gives new, all-order formulae for the collinear splitting function (in momentum space) and celestial OPE coefficients (in the conformal primary basis) of tree-level MHV gluon scattering. We obtain these results for both positive and negative helicity gluons, and for any incoming/outgoing kinematic configuration within the MHV sector.

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arXiv2022

Higher-spin Yang-Mills, amplitudes and self-duality

The existence of interacting higher-spin theories is tightly constrained by many no-go theorems. In this paper, we construct a chiral, higher-spin generalization of Yang-Mills theory in flat space which avoids these no-go theorems and has non-trivial tree-level scattering amplitudes with some higher-spin external legs. The fields and action are complex, so the theory is non-unitary and parity-violating, yet we find surprisingly compact formulae for all-multiplicity tree-level scattering amplitudes in the maximal helicity violating (MHV) sector, where the two negative helicity particles have identical but arbitrary spin. This is possible because the theory admits a perturbative expansion around its self-dual sector. Using twistor theory, we prove the classical integrability of this self-dual sector and show that it can be described on spacetime by an infinite tower of interacting massless scalar fields. We also give a twistor construction of the full theory, and use it to derive the formula for the MHV amplitude.

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arXiv2022

All order gravitational waveforms from scattering amplitudes

Waveforms are classical observables associated with any radiative physical process. Using scattering amplitudes, these are usually computed in a weak-field regime to some finite order in the post-Newtonian or post-Minkowskian approximation. Here, we use strong field amplitudes to compute the waveform produced in scattering of massive particles on gravitational plane waves, treated as exact nonlinear solutions of the vacuum Einstein equations. Notably, the waveform contains an infinite number of post-Minkowskian contributions, as well as tail effects. We also provide, and contrast with, analogous results in electromagnetism.

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