Gravitational spin Hamiltonians from the S matrix

By V. Vaidya. 2014

133 citations recorded by the source corpus.

We utilize generalized unitarity and recursion relations combined with effective field theory(EFT) techniques to compute spin dependent interaction terms for inspiralling binary systems in the post newtonian(PN) approximation. Using these methods offers great computational advantage over traditional techniques involving feynman diagrams, especially at higher orders in the PN expansion. As a specific example, we reproduce the spin-orbit interaction up to 2.5 PN order as also the leading order $S^2$(3PN) hamiltonian for an arbitrary massive object. We also obtain the unknown $S^3$(3.5PN) spin hamiltonian for an arbitrary massive object in terms of its low frequency linear response to gravitational perturbations, which was till now known only for a black hole. Furthermore, we derive the missing $S^4$ Hamiltonian at leading order(4PN) for an arbitrary massive object and establish that a minimal coupling of a massive elementary particle to gravity leads to a black hole structure. Finally, the Kerr metric is obtained as a series in $G_N$ by comparing the action of a test particle in the vicinity of a spinning black hole to the derived potential.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a32ace62ba4fabf15080154123a022304cb4ebd2

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Citations in the corpus

Spinning black hole binary dynamics, scattering amplitudes, and effective field theory (2020, methodology): “In the presence of spins, however, the known results from EFT or scattering angles are either limited to leading order in G or to special configurations of spins [23, 38, 59, 61, 63].”
On-shell heavy particle effective theories (2020, methodology): “Indeed, the effective field theory (EFT) of GR [2, 3] has been used extensively to compute classical corrections to the gravitational potential [3–11].”
The Effective Field Theorist's Approach to Gravitational Dynamics (2016, methodology): “4 in [156]), and in [102, 287] using so called on-shell methods, e.”
From boundary data to bound states (2019, background): “The inclusion of spin, both in the EFT approach [71–78] and in scattering amplitudes [40, 44, 48, 53, 79–82], introduces rich new structures.”
From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist) (2019, background): “Therefore, provided the matching discussed in [15–18] carries over to spin, as suggested in [19–26], the existence of this gauge is guarantee to all PM orders.”
Observables and amplitudes for spinning particles and black holes (2019, background): “However, from spin 1 particles we expect to be able to probe O(s2), or quadrupole, terms [4, 5, 9].”
Post-Minkowskian Hamiltonians in general relativity (2019, methodology): “Instead of expanding the action (1) in terms of ordinary Feynman rules, it pays to use modern amplitude methods to extract the needed non-analytic pieces in momentum transfer ~q through the appropriate cuts at loop level [2–4].”
Post-Minkowskian effective field theory for conservative binary dynamics (2020, unknown): “[3, 62–91].”
Scattering of spinning black holes from exponentiated soft factors (2018, methodology): “[27, 28], where the full tree-level amplitude for s = {12 , 1, 2} was computed in the first place.”
The simplest massive S-matrix: from minimal coupling to black holes (2018, background): “These include generalized unitarity methods [12, 13], double copy relations [14–17], and spinor-helicity variables [2, 3, 18–21].”
Holomorphic classical limit for spin effects in gravitational and electromagnetic scattering (2017, methodology): “respect to spin which are manifest in spinor helicity variables, and were previously argued in [26, 40, 60].”
Black hole binary dynamics from the double copy and effective theory (2019, methodology): “The EFT approach has led to new results for the PM potential at higher orders [20, 25].”
Double copy for massive quantum particles with spin (2019, methodology): “Focusing on analytical methods that use scattering amplitudes, there are by now a number of impressive results and techniques relevant to black-hole scattering [3–13].”