Scattering amplitudes for self-force

Using a recently developed effective field theory formalism for extreme mass ratios arXiv:2308.14832, we present a calculation of charged black hole scattering at third post-Minkowskian order. The charges and masses are kept arbitrary, and the result interpolates from the scattering of Schwarzschild to extremal charged black holes, and beyond to charged particles in electrodynamics — agreeing with previously reported results in all such limits. The computation of the radial action is neatly organized in powers of the mass ratio. The probe (0SF) contributions are readily computed by direct integration of the radial momentum, and we use the effective field theory to compute the subleading (1SF) contributions via background-field Feynman rules supplemented by an operator encoding recoil of the background. Together these contributions completely determine the conservative physics at order $$ \mathcal{O}\left({G}^3\right) $$ O G 3 .

Section: Introductionmentioning

confidence: 99%

Conservative scattering of Reissner-Nordström black holes at third post-Minkowskian order

Wilson-Gerow

2024

Gravitational self force from scattering amplitudes in curved space

Kosmopoulos,

Solon

2024

We employ scattering amplitudes in curved space to model the dynamics of a light probe particle with mass m orbiting in the background spacetime induced by a heavy gravitational source with mass M. Observables are organized as an expansion in m/M to all orders in G — the gravitational self-force expansion. An essential component of our analysis is the backreaction of the heavy source which we capture by including the associated light degrees of freedom. As illustration we consider a Schwarzschild background and verify geodesic motion as well as the first-order self-force correction to two-body scattering through $$\mathcal{O}$$(G3). Amplitudes in curved space offer several advantages, and further developments along these lines may advance the computation of gravitational-wave signals for extreme-mass-ratio inspirals.

Gravitational bound waveforms from amplitudes

Adamo,

Gonzo,

Ilderton

2024

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.