SUSY in the sky with gravitons

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.

On an exponential representation of the gravitational S-matrix

An exponential representation of the S-matrix provides a natural framework for understanding the semi-classical limit of scattering amplitudes. While sharing some similarities with the eikonal formalism it differs from it in details. Computationally, rules are simple because pieces that must be subtracted are given by combinations of unitarity cuts. Analyzing classical gravitational scattering to third Post-Minkowskian order in both maximal supergravity and Einstein gravity we find agreement with other approaches, including the contributions from radiation reaction terms. The kinematical relation for the two-body problem in isotropic coordinates follows immediately from this procedure, again with the inclusion of radiation reaction pieces up to third Post-Minkowskian order.

Rutherford’s extended formula and optimization of the gravity assists beam modelling in the Solar system

Rutherford’s formula for the scattering of charged α-particles in the Coulomb field can be easily generalized to the case of gravitational scattering. The extended Rutherford formula for the gravitational scattering is presented. One of the types of the gravitational scattering in the Solar system is the gravity assist maneuvers. In this paper, an effective gravitational scattering cross-section is introduced by analogy for them and the generalized Rutherford formula for gravitational scattering is presented out when performing gravity assists. Modern methods of the ballistic design of the interplanetary space flights using gravity assist maneuvers around planets [1-3] are associated with the need to calculate a lot of trajectories (i.e. of the phase beams). For their effective use it is necessary to study the structure of non-linear flyby gravitational scattering using the Rutherford’ formula and to construct the corresponding effective modelling using according regularized phase beams. It is shown that with using of such approach, it is possible to significantly increase the efficiency of the recurrent procedure for the gravity assists chains searching for ballistic scenarios of the modern interplanetary flights.

Gravity assists gravitational scattering and the perturbation rings in the Solar system

One of the types of gravitational scattering in the Solar system within the framework of the model of the restricted three-body problem (R3BP) is gravity assist maneuvers of the “particles of insignificant mass” [1] (spacecraft, asteroids, comets, etc.). For their description, a physical analogy with the beam scattering of charged α particles in a Coulomb field is useful. However, unlike the scattering of charged particles, there are external restrictions for the possibility of gravity assists executing related from the restricted size of planet’s sphere of influence. At the same time, internal restrictions for the gravity assists performance estimated by the effective radii of planets are known from the literature on R3BP [2] (gravitational capture by the planet, falling into it). They depend from the particle asymptotic velocity relative the planet. For obvious reasons, their influence cuts off the possibility of effective gravity assists performance [3]. In this work the generalized estimates of the sizes of the near-planetary regions (“perturbation rings”), falling into which is a necessary condition for the implementation of gravity assists, are presented. The detailed analysis shows that Neptune and Saturn have the characteristic “perturbation rings” of the largest sizes in the Solar system, and Jupiter occupies only the fourth place in this checklist.

The amplitude for classical gravitational scattering at third Post-Minkowskian order

We compute the scattering amplitude for classical black-hole scattering to third order in the Post-Minkowskian expansion, keeping all terms needed to derive the scattering angle to that order from the eikonal formalism. Our results confirm a conjectured relation between the real and imaginary parts of the amplitude by Di Vecchia, Heissenberg, Russo, and Veneziano, and are in agreement with a recent computation by Damour based on radiation reaction in general relativity.

The eikonal approach to gravitational scattering and radiation at $$ \mathcal{O} $$(G3)

Using $$ \mathcal{N} $$ N = 8 supergravity as a theoretical laboratory, we extract the 3PM gravitational eikonal for two colliding massive scalars from the classical limit of the corresponding elastic two-loop amplitude. We employ the eikonal phase to obtain the physical deflection angle and to show how its non-relativistic (NR) and ultra-relativistic (UR) regimes are smoothly connected. Such a smooth interpolation rests on keeping contributions to the loop integrals originating from the full soft region, rather than restricting it to its potential sub-region. This task is efficiently carried out by using the method of differential equations with complete near-static boundary conditions. In contrast to the potential-region result, the physical deflection angle includes radiation-reaction contributions that are essential for recovering the finite and universal UR limit implied by general analyticity and crossing arguments. We finally discuss the real emission of massless states, which accounts for the imaginary part of the 3PM eikonal and for the dissipation of energy-momentum. Adopting a direct approach based on unitarity and on the classical limit of the inelastic tree-level amplitude, we are able to treat $$ \mathcal{N} $$ N = 8 and General Relativity on the same footing, and to complete the conservative 3PM eikonal in Einstein’s gravity by the addition of the radiation-reaction contribution. We also show how this approach can be used to compute waveforms, as well as the differential and integrated spectra, for the different radiated massless fields.