Classical gravitational scattering from a gauge-invariant double copy

Picture yourself in the wave zone of a gravitational scattering event of two massive, spinning compact bodies (black holes, neutron stars or stars). We show that this system of genuine astrophysical interest enjoys a hidden $$ \mathcal{N} $$ N = 2 supersymmetry, at least to the order of spin-squared (quadrupole) interactions in arbitrary D spacetime dimensions. Using the $$ \mathcal{N} $$ N = 2 supersymmetric worldline action, augmented by finite-size corrections for the non-Kerr black hole case, we build a quadratic-in-spin extension to the worldline quantum field theory (WQFT) formalism introduced in our previous work, and calculate the two bodies’ deflection and spin kick to sub-leading order in the post-Minkowskian expansion in Newton’s constant G. For spins aligned to the normal vector of the scattering plane we also obtain the scattering angle. All D-dimensional observables are derived from an eikonal phase given as the free energy of the WQFT that is invariant under the $$ \mathcal{N} $$ N = 2 supersymmetry transformations.

Section: Discussionmentioning

confidence: 99%

Section: Jhep01(2022)027mentioning

confidence: 99%

SUSY in the sky with gravitons

Jakobsen

Mogull

Plefka

et al. 2022

“…Higher order corrections to Einstein's Quadrupole formula in the context of the quasi-circular orbit general relativistic two-body problem -needed to enable such detections -have traditionally been obtained in the post-Newtonian (PN) [3,4] formalism, within numerical relativity [5] and JHEP01(2022)006 black hole perturbation theory [6,7], as well as models combining these approaches [8][9][10]. More recently, however, efforts have been focused on the BBH scattering problem, in order to connect classical computations performed in the context of post-Minkowskian (PM) theory [11][12][13][14][15][16][17][18][19][20][21][22][23][24], with those approaches based on the classical limit of QFT scattering amplitudes .…”

Section: Introductionmentioning

confidence: 99%

Post-Newtonian waveforms from spinning scattering amplitudes

Bautista

Siemonsen

2022

We derive the classical gravitational radiation from an aligned spin binary black hole on closed orbits, using a dictionary built from the 5-point QFT scattering amplitude of two massive particles exchanging and emitting a graviton. We show explicitly the agreement of the transverse-traceless components of the radiative linear metric perturbations — and the corresponding gravitational wave energy flux — at future null infinity, derived from the scattering amplitude and those derived utilizing an effective worldline action in conjunction with multipolar post-Minkowskian matching. At the tree-level, this result holds at leading orders in the black holes’ velocities and up to quadratic order in their spins. At sub-leading order in black holes’ velocities, we demonstrate a matching of the radiation field for quasi-circular orbits in the no-spin limit. At the level of the radiation field, and to leading order in the velocities, there exists a one-to-one correspondence between the binary black hole mass and current quadrupole moments, and the scalar and linear-in-spin scattering amplitudes, respectively. Therefore, we show explicitly that waveforms, needed to detect gravitational waves from inspiraling binary black holes, can be derived consistently, to the orders considered, from the classical limit of quantum scattering amplitudes.

“…Scattering bodies are accompanied by emission of gravitational Bremsstrahlung radiation [17,[59][60][61][62][63][64], which is the unbound analog of the gravitational waves emitted by inspiral binaries and is suppressed by three powers of G. Although radiation reaction effects were thoroughly investigated in the past in the Regge limit (i.e., when the centerof-mass energy is much larger than the momentum transfer) [65][66][67][68] or in association to the loss of angular momentum in the collision [69][70][71][72][73][74], the full leading-order emitted momentum has been obtained only very recently in [75,76] via the formalism of [77], which derives classical observables from quantum scattering (see also [78,79] for extensions of the formalism of [77] to spin and classical observables in Yang-Mills theories), and in [80] using the eikonal approach to classical gravitational scattering. These calculations require evaluating the classical limit of relevant two-loop Feynman integrals, that can be solved by combining different techniques borrowed from particle physics, as shown in [81], namely reduction to master integrals by Integration-by-Parts (IBP) identities [82][83][84] and differential equations [85][86][87][88] to solve the latter, using the near-static regime as initial conditions.…”

Section: Introductionmentioning

confidence: 99%

Radiated momentum in the post-Minkowskian worldline approach via reverse unitarity

Riva

Vernizzi

2021

We compute the four-momentum radiated during the scattering of two spinless bodies, at leading order in the Newton’s contant G and at all orders in the velocities, using the Effective Field Theory worldline approach. Following [1], we derive the conserved stress-energy tensor linearly coupled to gravity generated by localized sources, at leading and next-to-leading order in G, and from that the classical probability amplitude of graviton emission. The total emitted momentum is obtained by phase-space integration of the graviton momentum weighted by the modulo squared of the radiation amplitude. We recast this as a two-loop integral that we solve using techniques borrowed from particle physics, such as reverse unitarity, reduction to master integrals by integration-by-parts identities and canonical differential equations. The emitted momentum agrees with recent results obtained by other methods. Our approach provides an alternative way of directly computing radiated observables in the post-Minkowskian expansion without going through the classical limit of scattering amplitudes.