Observables and amplitudes for spinning particles and black holes

Maybee, Ben; O’Connell, Donal; Vines, Justin

doi:10.1007/jhep12(2019)156

Cited by 245 publications

(291 citation statements)

References 98 publications

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“…There is also the intriguing connection between elementary particles and black holes, e.g. [19][20][21][22][23][24][25][26]. We conclude our paper with a few words on these issues.…”

Section: Discussionmentioning

confidence: 91%

From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist)

Kälin

Porto

2020

J. High Energ. Phys.

197

261

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We recently introduced in [1910.03008] 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: ∆Φ(J, E) = χ(J, E) + χ(−J, E), via analytic continuation in angular momentum and binding energy. Using explicit expressions from [1910.03008], 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 [1910.03008] 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 the 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 [1910.03008] 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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“…There is also the intriguing connection between elementary particles and black holes, e.g. [19][20][21][22][23][24][25][26]. We conclude our paper with a few words on these issues.…”

Section: Discussionmentioning

confidence: 91%

From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist)

Kälin

Porto

2020

J. High Energ. Phys.

197

261

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Section: Arxiv:190907361v1 [Gr-qc] 16 Sep 2019mentioning

confidence: 99%

“…Subsequently, using and extending a formalism for extracting classical observables from on-shell amplitudes developed by Kosower, Maybee and O'Connell [52], the generalization to spinning particles was considered by Maybee et al [53]. It was shown in [53] through O(a 2 ), and then by Ochirov et al in [54] through O(a ∞ ) for both spins, that the arbitrary-spin tree amplitudes from [40,42,43] lead (by a well-motivated procedure) to the covariant scattering holonomy results for genericspin binary BHs at O(G 1 a ∞ ) derived by one of the authors in [15], matching at O(G 1 a 1 ) results of Bini and Damour [10]. A scalar-probe limit of the same genericspin scattering holonomy, namely the O(G 1 a ∞ ) impulse (change in momentum) for a generic (weakly deflected) unbound geodesic in the Kerr spacetime, has also been produced from an elegant double copy of the amplitude for the analogous electromagnetic case, a test charge in the " √ Kerr " electromagnetic field in flat spacetime, by Arkani-Hamed, Huang and O'Connell [55]; see also [56].…”

Section: Arxiv:190907361v1 [Gr-qc] 16 Sep 2019mentioning

confidence: 99%

“…Kavanagh, Ottewill, and Wardell [62] have computed the linear-in-mass-ratio corrections δU to the Kerrgeodesic result z (0) (Ω) for Detweiler's [78] redshift invariant for circular equatorial orbits in a perturbed Kerr background, via methods of solving the Teukolsky equation [79] due to Mano, Suzuki and Takasugi [80,81]. For a Kerr background with mass m and spin S = m 2â , in terms of the orbital frequency Ω with y = (GmΩ) 2/3 , they find In the rearrangement of terms (n) as suggested by the colors of Figure 1 in [13], coinciding with rows in (46) and diagonals in (53), the purple, blue and green terms are 1 y δU (0) = −1, according to [62]. Bini, Damour, Geralico, Kavanagh, and van de Meent [63] have computed the first-order self-force correction δψ to the precession frequency for circular equatorial Kerr geodesics to be given by (51) with…”

Section: Redshift and Precession Frequency Through Linear Deviations mentioning

confidence: 99%

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

Siemonsen

Vines

2020

Phys. Rev. D

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It has been suggested that amplitudes for quantum higher-spin massive particles exchanging gravitons lead, via a classical limit, to results for scattering of spinning black holes in general relativity, when the massive particles are in a certain way minimally coupled to gravity. Such limits of such amplitudes suggest, at least at lower orders in spin, up to second order in the gravitational constant G, that the classical aligned-spin scattering function for an arbitrary-mass-ratio two-spinning-blackhole system can be obtained by a simple kinematical mapping from that for a spinning test black hole scattering off a stationary background Kerr black hole. Here we test these suggestions, at orders beyond the reach of the post-Newtonian and post-Minkowskian results used in their initial partial verifications, by confronting them with results from general-relativistic "self-force" calculations of the linear perturbations of a Kerr spacetime sourced by a small orbiting body, here considering only results for circular orbits in the equatorial plane. We translate between scattering and circular-orbit results by assuming the existence of a local-in-time canonical Hamiltonian governing the conservative dynamics of generic (bound and unbound) aligned-spin orbits, while employing the associated first law of spinning binary mechanics. We confirm, through linear order in the mass ratio, some previous conjectures which would begin to fill in the spin-dependent parts of the conservative dynamics for arbitrary-mass-ratio aligned-spin binary black holes at the fourth-and-a-half and fifth post-Newtonian orders.

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“…Extracting classical gravitational physics from quantum field theories has a long history [2][3][4]. More recently the modern on-shell scattering amplitudes program has provided a number of tools that can be used to greatly simplify calculations of gravitational quantities, notably the KLT relations and the BCJ double copy [5][6][7][8][9], as well as those related specifically to classical observables [10][11][12]. While the original aim of the double copy program was to simplify loop computations in gravity, it has found many uses in classical gravity, from metric reconstruction [13][14][15][16][17][18][19][20] to gravitational wave physics [21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Kerr-Newman from minimal coupling

Moynihan¹

2020

J. High Energ. Phys.

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We show that at 1PN all four-dimensional black hole solutions in asymptotically flat spacetimes can be derived from leading singularities involving minimally coupled three-particle amplitudes. Furthermore, we show that the rotating solutions can be derived from their non-rotating counterparts by a spin-factor deformation of the relevant minimally coupled amplitudes. To show this, we compute the tree-level and one-loop leading singularities for a heavy charged source with generic spin s. We compute the metrics both with and without a spin factor and show that we get both the Kerr-Newman and Reissner-Nordström solutions respectively. We then go on to compute the impulse imparted to the probe particle in the infinite spin limit and show that the spin factor induces a complex deformation of the impact parameter, as was recently observed for Kerr black holes in [1]. We interpret these observations as being the on-shell avatar of the Janis-Newman algorithm for charged black holes.

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Observables and amplitudes for spinning particles and black holes

Cited by 245 publications

References 98 publications

From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist)

From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist)

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

Kerr-Newman from minimal coupling

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