Gravitational spin Hamiltonians from the S matrix

Abstract

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.

version2, typos fixed, references added, results unchanged

References in corpus (6)

• Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling
• Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach
• Search for Gravitational Waves from Binary Black Hole Inspiral, Merger and Ringdown in LIGO-Virgo Data from 2009-2010
• ADM canonical formalism for gravitating spinning objects
• Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincaré invariance
• Reduced Hamiltonian for next-to-leading order Spin-Squared Dynamics of General Compact Binaries

Cited by in corpus (12)

• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries
• Classical observables from coherent-spin amplitudes
• Kerr-Newman from Minimal Coupling
• Strings, extended objects, and the classical double copy
• Loop-Level Double-Copy for Massive Quantum Particles
• Quantum corrections to frame-dragging in scattering amplitudes
• Mimicking Kerr's multipole moments
• $S$-matrix approach to general gravity and beyond
• Quantum point particle approximation of spinning black holes and compact stars