Waveforms from amplitudes

Self Cite

We explore the celestial holography proposal for non-trivial asymptotically flat backgrounds including the Coulomb field of a static and spinning point charge, their gravitational counterparts described by the Schwarzschild and Kerr metrics, as well as the Aichelburg-Sexl shockwave and spinning shockwave geometries and their electromagnetic cousins. We compute celestial two-point amplitudes on these Kerr-Schild type backgrounds which have the desirable feature, due to the presence of an external source, that they are non-vanishing for general operator positions and are not constrained by the kinematic delta functions of flat space celestial CFT correlators. Of particular interest is the case of shockwave backgrounds where the two-point scattering amplitude of massless scalars can be interpreted as a standard CFT three-point correlator between two massless asymptotic states and a conformal primary shockwave operator. We furthermore show that the boundary on-shell action for general backgrounds becomes the generating functional for tree-level correlation functions in celestial CFT. Finally, we derive (conformal) Faddeev-Kulish dressings for particle-like backgrounds which remove all infrared divergent terms in the two-point functions to all orders in perturbation theory.

Section: Jhep10(2022)073mentioning

confidence: 99%

“…In general, the scattering of a wave on a background may require considering higher-point amplitudes but we are interested here in the leading connected amplitude contribution. For classical wave scattering, this can be made explicit by using coherent states[69] and in such case only the four-point amplitude contributes at all orders.…”

mentioning

confidence: 99%

Celestial holography on Kerr-Schild backgrounds

Gonzo

McLoughlin

Puhm

2022

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“…Other approaches have focused instead on effective field theory techniques for the derivation of these solutions [7,8] or the use of one-point functions for the extraction of the large distance behaviour [9]. More recently, the relevance of three-point amplitudes for the derivation of classical solutions has been emphasised within the framework of classical JHEP02(2023)107 observables [10,11], using off-shell techniques in Lorentzian signature [12] and on-shell ones in split signature [13,14], while twistor methods have also been employed to provide interesting results related to classical solutions [15,16].…”

Section: Introductionmentioning

confidence: 99%

The ultrarelativistic limit of Kerr

Adamo

Cristofoli

Tourkine

2023

Self Cite

The massless (or ultrarelativistic) limit of a Schwarzschild black hole with fixed energy was determined long ago in the form of the Aichelburg-Sexl shockwave, but the status of the same limit for a Kerr black hole is less clear. In this paper, we explore the ultrarelativistic limit of Kerr in the class of Kerr-Schild impulsive pp-waves by exploiting a relation between the metric profile and the eikonal phase associated with scattering between a scalar and the source of the metric. This gives a map between candidate metrics and tree-level, 4-point scattering amplitudes. At large distances from the source, we find that all candidates for the massless limit of Kerr in this class do not have spin effects. This includes the metric corresponding to the massless limit of the amplitude for gravitational scattering between a scalar and a massive particle of infinite spin. One metric, discovered by Balasin and Nachbagauer, does have spin and finite size effects at short distances, leading to a remarkably compact scattering amplitude with many interesting properties. We also discuss the classical single copy of the ultrarelativistic limit of Kerr in electromagnetism.

“…The hierarchy λ a is only needed for the conceptual foundation of geometric optics and is irrelevant for any of the analyses in this paper. In terms of wavepackets, there is an additional scale hierarchy λ ξ b where ξ is the wavepacket size[93]. JWK would like to thank Donal O'Connell for discussions on this point.…”

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confidence: 99%

Gravitational Faraday effect from on-shell amplitudes

Chen

Chung

Huang

et al. 2022

Effects of massive object’s spin on massive-massless 2 → 2 classical scattering is studied. Focus is set on the less-considered dimensionless expansion parameter λ/b, where λ is the massless particle’s wavelength and b is the impact parameter. Corrections in λ/b start to appear from $$ \mathcal{O} $$ O (G2), with leading correction terms tied to the gravitational Faraday effect, which is a special case of the Lense-Thirring effect. We compute the eikonal phase up to $$ \mathcal{O} $$ O (G2) and extract spin effect on the scattering angle and time delay up to 14th order in spin. The gravitational Faraday effect at linear order in spin [1] is reproduced by λ/b correction terms, which we compute to higher orders in spin. We find that the equivalence principle, or universality, holds up to NLO for general spinning bodies, i.e. away from geometric optics limit. Furthermore, in the black hole limit, we confirm the absence of particular spin structure observed [2–8], along with the associated shift symmetry [7], and argue that it holds to arbitrary spin order at $$ \mathcal{O} $$ O (G2) in the massless probe limit.