From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist)
By G. Kalin, Rafael A. Porto. Journal of High Energy Physics, 2019
173 citations recorded by the source corpus.
We recently introduced in [ 9 ] a boundary-to-bound dictionary between gravitational scattering data and observables for bound states of non-spinning bodies. In this paper, we elaborate further on this holographic map. We start by deriving the following — remarkably simple — formula relating the periastron advance to the scattering angle: ΔΦ J E = χ J E + χ − J E $$ \Delta \Phi \left(J,\mathcal{E}\right)=\upchi \left(J,\mathcal{E}\right)+\upchi \left(-J,\mathcal{E}\right) $$ , via analytic continuation in angular momentum and binding energy. Using explicit expressions from [ 9 ], we confirm its validity to all orders in the Post-Minkowskian (PM) expansion. Furthermore, we reconstruct the radial action for the bound state directly from the knowledge of the scattering angle. The radial action enables us to write compact expressions for dynamical invariants in terms of the deflection angle to all PM orders, which can also be written as a function of the PM-expanded amplitude. As an example, we reproduce our result in [ 9 ] for the periastron advance, and compute the radial and azimuthal frequencies and redshift variable to two-loops. Agreement is found in the overlap between PM and Post-Newtonian (PN) schemes. Last but not least, we initiate the study of our dictionary including spin. We demonstrate that the same relation between deflection angle and periastron advance applies for aligned-spin contributions, with J the (canonical) total angular momentum. Explicit checks are performed to display perfect agreement using state-of-the-art PN results in the literature. Using the map between test- and two-body dynamics, we also compute the periastron advance up to quadratic order in spin, to one-loop and to all orders in velocity. We conclude with a discussion on the generalized ‘impetus formula’ for spinning bodies and black holes as ‘elementary particles’. Our findings here and in [ 9 ] imply that the deflection angle already encodes vast amount of physical information for bound orbits, encouraging independent derivations using numerical and/or self-force methodologies.
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Citations in the corpus
- Post-Minkowskian effective field theory for conservative binary dynamics (2020, methodology): “ j2 ! = j+ (2 2 1) p 1 2 + 3 4j (5 2 1) : (4.35) From here, following the B2B dictionary reviewed in x2, we arrive at the same 2PM values for the gravitational observables for bound orbits derived in [1,2] from the classical limit of the scattering amplitude/angle, namely 2PM 2ˇ = 3 4j2 (5 2 1) ; (4”
- Classical black hole scattering from a worldline quantum field theory (2020, methodology): “etermine its conservative two-body potential [85,95]. The so-obtained eective potential is then used to compute observables such as the scattering angle or the periastron advance in the bound system [64,96,97]. Both approaches | involving the worldline EFT and modern scattering amplitudes | agree on”
- Spinning black hole binary dynamics, scattering amplitudes, and effective field theory (2020, methodology): “A very interesting question is whether there exist, in general, simple and direct relations between physical quantities and suitably-defined finite parts of amplitudes scattering amplitudes analogous to the one for the spinless or aligned spin case [10, 15, 39, 59].”