The ultrarelativistic limit of Kerr

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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.

Section: Discussionmentioning

confidence: 99%

Large gauge effects and the structure of amplitudes

Cristofoli

Asaad

Ilderton

et al. 2023

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“…This is a topic which has been considered many times in the past, often by using a ladder approximation in the Bethe-Salpeter equation [46][47][48], but this is not sufficient to establish a direct connection to classical bound states when relativistic effects are relevant. 1 Other approaches (e.g., making use of 'generalized ladder' approximations) have gotten closer [49][50][51][52][53][54][55][56], but all these attempts are at least partially incomplete due to lacking an appropriate classical limit at amplitude level [7,57] or failing to recover probe limit results [13,14,[58][59][60][61][62][63] at leading order in the resummation.…”

Section: A Exponentiation Of the 3-pt Function For The Classical Lore...mentioning

confidence: 99%

Bethe-Salpeter equation for classical gravitational bound states

Adamo

Gonzo

2023

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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.

Aligned fields double copy to Kerr-NUT-(A)dS

Chawla

Keeler

2023

We find Abelian gauge fields that double copy to a large class of black hole spacetimes with spherical horizon topology known as the Kerr-NUT-(A)dS family. Using a multi-Kerr-Schild prescription, we extend the previously-known double copy structure for arbitrarily rotating general dimension black holes, to include NUT charges and an arbitrary cosmological constant. In all cases, these single copy gauge fields are ‘aligned fields’, because their nonzero components align with the principal tensor which generates the Killing structure of the spacetime. In five dimensions, we additionally derive the same single-copy field strengths via the Weyl double copy procedure.