Tidal effects for spinning particles

Abstract

Expanding on the recent derivation of tidal actions for scalar particles, we present here the action for a tidally deformed spin-1/2 particle. Focusing on operators containing two powers of the Weyl tensor, we combine the Hilbert series with an on-shell amplitude basis to construct the tidal action. With the tidal action in hand, we compute the leading-post-Minkowskian tidal contributions to the spin-1/2–spin-1/2 amplitude, arising at $$ \mathcal{O} $$ O (G2). Our amplitudes provide evidence that the observed long range spin-universality for the scattering of two point particles extends to the scattering of tidally deformed objects. From the scattering amplitude we find the conservative two-body Hamiltonian, linear and angular impulses, eikonal phase, spin kick, and aligned-spin scattering angle. We present analogous results in the electromagnetic case along the way.

Quadratic-in-spin Hamiltonian at $$ \mathcal{O} $$(G2) from scattering amplitudes

“…Recently, ref. [41] also remarked that finite-size effects spoil the above expectation. Interestingly, for the Kerr black-hole case (C ES 2 = 1) the amplitude indeed depends on the linear combination q 2 S 2 1 − (q • S 1 ) 2 .…”

“…This is in line with a recent observation in ref. [41], that this equality fails to hold in the presence of tidal finite-size effects.…”

“…Refs. [40][41][42][43][44][45][46] considered tidal deformations of the astrophysical objects. In the present paper we explore a different direction and focus on effects due to the spin of the compact objects.…”

A worldsheet for Kerr

“…We do not know whether the worldsheet structure persists when higher-order operators, involving two or more powers of the Riemann curvature (or electromagnetic field strength), are included. But we can certainly hope that the surprising simplicity of Kerr persists to higher orders -the computation of observables from loop-level amplitudes for particles with spin [24,25,40,71] certainly indicates that further progress can be made. Meanwhile precision calculations reliant on the effective action in (2.1) require including higher-dimension operators in the action [108][109][110].…”

“…Although amplitudes are rooted in quantum field theory, in recent years there has been an explosion of interest in applications of amplitudes to classical physics [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. This is motivated by the applicability of the results for elastic and inelastic [45][46][47][48][49][50][51][52][53][54][55][56][57] gravitational scattering of two massive particles to gravitational-wave physics [58][59][60][61][62][63][64][65][66][67][68][69][70][71][72], as JHEP03(2021)201 well as by the search for the underlying principles behind the double-copy relationship between gauge theory and gravity [4,…”