Test black holes, scattering amplitudes, and perturbations of Kerr spacetime

200

199

We develop an Effective Field Theory (EFT) formalism to solve for the conservative dynamics of binary systems in gravity via Post-Minkowskian (PM) scattering data. Our framework combines a systematic EFT approach to compute the deflection angle in the PM expansion, together with the ‘Boundary-to-Bound’ (B2B) dictionary introduced in [1, 2]. Due to the nature of scattering processes, a remarkable reduction of complexity occurs both in the number of Feynman diagrams and type of integrals, compared to a direct EFT computation of the potential in a PM scheme. We provide two illustrative examples. Firstly, we compute all the conservative gravitational observables for bound orbits to 2PM, which follow from only one topology beyond leading order. The results agree with those in [1, 2], obtained through the ‘impetus formula’ applied to the classical limit of the one loop amplitude in Cheung et al. [3]. For the sake of comparison we reconstruct the conservative Hamiltonian to 2PM order, which is equivalent to the one derived in [3] from a matching calculation. Secondly, we compute the scattering angle due to tidal effects from the electric- and magnetic-type Love numbers at leading PM order. Using the B2B dictionary we then obtain the tidal contribution to the periastron advance. We also construct a Hamiltonian including tidal effects at leading PM order. Although relying on (relativistic) Feynman diagrams, the EFT formalism developed here does not involve taking the classical limit of a quantum amplitude, neither integrals with internal massive fields, nor additional matching calculations, nor spurious (‘super-classical’) infrared singularities. By construction, the EFT approach can be automatized to all PM orders.

Section: Jhep11(2020)106mentioning

confidence: 99%

Post-Minkowskian effective field theory for conservative binary dynamics

Kälin

Porto

2020

200

199

“…via an effective matching to the scattering angle [43,60,61]. An alternative venue was also pursued in [62], where it was shown how the scattering angle to 2PM can be obtained from the test-particle limit, and later used in [63] to construct a (local-in-time) Hamiltonian for circular orbits. In all of these cases, a Hamiltonian (or equivalent) has played a central role; or a resummed version in the effective one-body formalism [64].…”

Section: Introductionmentioning

confidence: 99%

From boundary data to bound states

Kälin

Porto

2020

260

339

We introduce a-somewhat holographic-dictionary between gravitational observables for scattering processes (measured at the boundary) and adiabatic invariants for bound orbits (in the bulk), to all orders in the Post-Minkowskian (PM) expansion. Our map relies on remarkable connections between the relative momentum of the twobody problem, the classical limit of the scattering amplitude and the deflection angle in hyperbolic motion. These relationships allow us to compute observables for generic orbits (such as the periastron advance ∆Φ) through analytic continuation, via a radial action depending only on boundary data. A simplified (more geometrical) map can be obtained for circular orbits, enabling us to extract the orbital frequency as a function of the (conserved) binding energy, Ω(E), directly from scattering information. As an example, using the results in Bern et al. [36, 37], we readily derive Ω(E) and ∆Φ(J, E) to two-loop orders. We also provide closed-form expressions for the orbital frequency and periastron advance at tree-level and one-loop order, respectively, which capture a series of exact terms in the Post-Newtonian expansion. We then perform a partial PM resummation, using a no-recoil approximation for the amplitude. This limit is behind the map between the scattering angle for a test-particle and the two-body dynamics to 2PM. We show that it also captures a subset of higher order terms beyond the test-particle limit. While a (rather lengthy) Hamiltonian may be derived as an intermediate step, our map applies directly between gauge invariant quantities. Our findings provide a starting point for an alternative approach to the binary problem. We conclude with future directions and some speculations on the classical double copy.

“…Given the expected improvements in detector sensitivity, it will be extremely important in the future to have high-precision theoretical predictions from General Relativity. To this aim the use of quantum field theory amplitudes to extract the post-Minkowskian (PM) expansion of General Relativity has recently gained considerable momentum [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], and progress is now also being made on extensions to spinning objects [22][23][24][25][26][27][28][29][30][31]. The underlying physical motivation for this approach lies in the observation that, during the early stages of a merger event, when the two compact objects are still far apart, gravitational interactions are weak and can be conveniently treated JHEP07(2020)122 in a weak-coupling approximation.…”

Section: Introductionmentioning

confidence: 99%

Second-order post-Minkowskian scattering in arbitrary dimensions

Cristofoli

Damgaard

Vecchia

et al. 2020

126

We extract the long-range gravitational potential between two scalar particles with arbitrary masses from the two-to-two elastic scattering amplitude at 2nd Post-Minkowskian order in arbitrary dimensions. In contrast to the four-dimensional case, in higher dimensions the classical potential receives contributions from box topologies. Moreover, the kinematical relation between momentum and position on the classical trajectory contains a new term which is quadratic in the tree-level amplitude. A precise interplay between this new relation and the formula for the scattering angle ensures that the latter is still linear in the classical part of the scattering amplitude, to this order, matching an earlier calculation in the eikonal approach. We point out that both the eikonal exponentiation and the reality of the potential to 2nd post-Minkowskian order can be seen as a consequence of unitarity. We finally present closed-form expressions for the scattering angle given by leading-order gravitational potentials for dimensions ranging from four to ten.