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Quadratic-in-Spin Hamiltonian at $\mathcal{O}(G^2)$ from Scattering Amplitudes

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arxiv 2102.10137 v1 pith:EBC6A3K7 submitted 2021-02-19 hep-th gr-qc

Dimitrios Kosmopoulos , Andres Luna This is my paper · ORCID
classification hep-thgr-qc
keywords scatteringamplitudesconsiderhamiltonianmathcalquadratic-in-spinspinningbern
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

We obtain the quadratic-in-spin terms of the conservative Hamiltonian describing the interactions of a binary of spinning bodies in General Relativity through $\mathcal{O}(G^2)$ and to all orders in velocity. Our calculation extends a recently-introduced framework based on scattering amplitudes and effective field theory to consider non-minimal coupling of the spinning objects to gravity. At the order that we consider, we establish the validity of the formula proposed in \cite{Bern:2020buy} that relates the impulse and spin kick in a scattering event to the eikonal phase.

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Cited by 7 Pith papers

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  1. Dynamical Love Numbers for Black Holes and Beyond from Shell Effective Field Theory

    hep-th 2025-12 accept novelty 8.0 of 10

    A shell-based EFT computes scalar Love numbers for Schwarzschild black holes through O(G^9) and conjectures an all-orders Riemann-zeta structure.

  2. Spinning the Probe in Kerr with WQFT

    hep-th 2025-06 conditional novelty 8.0 of 10

    Using worldline quantum field theory, the authors derive the impulse and spin kick for a spinning probe scattering in Kerr spacetime through seventh physical post-Minkowskian order.

  3. Searching for Kerr in string amplitudes

    hep-th 2025-06 conditional novelty 7.0 of 10

    Infinite-spin limits of three-point open-string amplitudes along sub-leading trajectories generate new Bessel-function currents, but the two-harmonic tilted trajectory does not match the two-mode classical string solu...

  4. Gravitational Bremsstrahlung in Black-Hole Scattering at $\mathcal{O}(G^3)$: Quadratic-in-Spin Effects

    hep-th 2025-05 accept novelty 7.0 of 10

    First computation of the O(G^3 S^2) momentum-space gravitational waveform for two scattering spinning black holes, plus the leading three-body spinning waveform.

  5. First Look at Quartic-in-Spin Binary Dynamics at Third Post-Minkowskian Order

    hep-th 2025-02 conditional novelty 7.0 of 10

    The O(G^3) conservative and radiation-reaction classical observables for spinning black-hole scattering are extended to quartic order in spin, with all-order-in-spin radiation reaction beyond the aligned-spin limit.

  6. One-Loop Observables to Higher Order in Spin

    hep-th 2024-12 conditional novelty 6.0 of 10

    New one-loop formulas express the momentum impulse and spin kick of two scattered spinning bodies directly in terms of the eikonal phase, valid to all orders in spin and independent of the spin supplementary condition.

  7. Dictionary revision for mapping boundary data to bound states

    gr-qc 2025-05 conditional novelty 5.0 of 10

    A revised boundary-to-bound dictionary, using p_inf^2 -> p_inf^2 e^(-i pi), makes fourth-order post-Minkowskian bound-orbit observables real and matches numerical relativity binding energies for mass ratios 1 and 10.

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