Next-to-leading order gravitational spin1-spin2 coupling with Kaluza-Klein reduction

Abstract

We use the recently proposed Kaluza-Klein (KK) reduction over the time dimension, within an effective field theory (EFT) approach, to calculate the next to leading order (NLO) gravitational spin1-spin2 interaction between two spinning compact objects. It is shown here that to NLO in the spin1-spin2 interaction, the reduced KK action within the stationary approximation is sufficient to describe the gravitational interaction, and that it simplifies calculation substantially. We also find here that the gravito-magnetic vector field defined within the KK decomposition of the metric mostly dominates the mediation of the interaction. Our results coincide with those calculated in the ADM Hamiltonian formalism, and we provide another explanation for the discrepancy with the result previously derived within the EFT approach, thus demonstrating clearly the equivalence of the ADM Hamiltonian formalism and the EFT action approach.

12 pages, revtex4-1, 3 figures; v2: reference added; v3: edited, section 3 elaborated; v4: published

References in corpus (12)

• Spin(1)Spin(2) Effects in the Motion of Inspiralling Compact Binaries at Third Order in the Post-Newtonian Expansion
• The Hyperfine Einstein-Infeld-Hoffmann Potential
• The next-to-leading order gravitational spin(1)-spin(2) dynamics in Hamiltonian form
• ADM canonical formalism for gravitating spinning objects
• Non-Relativistic Gravitation: From Newton to Einstein and Back
• Classical Effective Field Theory and Caged Black Holes
• Les Houches Lectures on Effective Field Theories and Gravitational Radiation
• Reduced Hamiltonian for next-to-leading order Spin-Squared Dynamics of General Compact Binaries
• Asymptotics of d-dimensional Kaluza-Klein black holes: beyond the Newtonian approximation
• Comment on recent papers regarding next-to-leading order spin-spin effects in gravitational interaction
• New results at 3PN via an effective field theory of gravity
• Comment on `On the next-to-leading order gravitational spin(1)-spin(2) dynamics' by J. Steinhoff et al

Cited by in corpus (86)

• Amplitudes, Observables, and Classical Scattering
• The Effective Field Theorist's Approach to Gravitational Dynamics
• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
• Prototype effective-one-body model for nonprecessing spinning inspiral-merger-ringdown waveforms
• Classical black hole scattering from a worldline quantum field theory
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• Quadratic-in-spin effects in the orbital dynamics and gravitational-wave energy flux of compact binaries at the 3PN order
• Ready-to-use post-Newtonian gravitational waveforms for binary black holes with non-precessing spins: An update
• Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order
• Gravitational spin Hamiltonians from the S matrix
• The complete non-spinning effective-one-body metric at linear order in the mass ratio
• The tail effect in gravitational radiation-reaction: time non-locality and renormalization group evolution
• Effective field theory methods to model compact binaries
• Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach
• Binary dynamics from spin1-spin2 coupling at fourth post-Newtonian order
• Extending the effective-one-body Hamiltonian of black-hole binaries to include next-to-next-to-leading spin-orbit couplings
• Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries
• Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
• Quadratic-in-Spin Hamiltonian at $\mathcal{O}(G^2)$ from Scattering Amplitudes
• Next-to-next-to-leading order spin-orbit effects in the equations of motion of compact binary systems
• Compton Black-Hole Scattering for $s\le 5/2$
• Classical potential for general spinning bodies
• Next-to-next-to-leading order gravitational spin-squared potential via the effective field theory for spinning objects in the post-Newtonian scheme
• Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals
• Binary Dynamics Through the Fifth Power of Spin at $\mathcal{O}(G^2)$
• The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
• Multipole expansion at the level of the action
• Tail terms in gravitational radiation reaction via effective field theory
• The 2PM Hamiltonian for binary Kerr to quartic in spin
• Conservative Binary Dynamics with a Spinning Black Hole at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Influence of internal structure on the motion of test bodies in extreme mass ratio situations
• Tail-induced spin-orbit effect in the gravitational radiation of compact binaries
• Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post-Newtonian scheme
• Canonical Formulation of Spin in General Relativity
• Canonical Hamiltonian for an extended test body in curved spacetime: To quadratic order in spin
• Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians
• Next-to-leading tail-induced spin-orbit effects in the gravitational radiation flux of compact binaries
• Next-to-next-to-leading order post-Newtonian spin-orbit Hamiltonian for self-gravitating binaries
• Next-to-next-to-leading order post-Newtonian spin(1)-spin(2) Hamiltonian for self-gravitating binaries
• Radiation reaction for spinning bodies in effective field theory II: Spin-spin effects
• Radiation reaction for spinning bodies in effective field theory I: Spin-orbit effects
• N${}^3$LO gravitational spin-orbit coupling at order $G^4$
• First Law of Mechanics for Black Hole Binaries with Spins
• NNNLO gravitational quadratic-in-spin interactions at the quartic order in G
• Conservative corrections to the innermost stable circular orbit (ISCO) of a Kerr black hole: a new gauge-invariant post-Newtonian ISCO condition, and the ISCO shift due to test-particle spin and the gravitational self-force
• Spin-multipole effects in binary black holes and the test-body limit
• NLO gravitational quartic-in-spin interaction
• EFTofPNG: A package for high precision computation with the Effective Field Theory of Post-Newtonian Gravity
• Comparing space+time decompositions in the post-Newtonian limit
• Complete conservative dynamics for inspiralling compact binaries with spins at the fourth post-Newtonian order
• Motion and gravitational wave forms of eccentric compact binaries with orbital-angular-momentum-aligned spins under next-to-leading order in spin-orbit and leading order in spin(1)-spin(2) and spin-squared couplings
• Gravitational Spin-Orbit Hamiltonian at NNNLO in the post-Newtonian framework
• Spin contributions to the gravitational-waveform modes for spin-aligned binaries at the 3.5PN order
• Completing the Fifth PN Precision Frontier via the EFT of Spinning Gravitating Objects
• N${}^3$LO Quadratic-in-Spin Interactions for Generic Compact Binaries
• N${}^3$LO Spin-Orbit Interaction via the EFT of Spinning Gravitating Objects
• Gravitational Quadratic-in-Spin Hamiltonian at NNNLO in the post-Newtonian framework
• Quadratic-in-spin interactions at fifth post-Newtonian order probe new physics
• Fourth post-Newtonian effective-one-body Hamiltonians with generic spins
• Testing the multipole structure and conservative dynamics of compact binaries using gravitational wave observations: The spinning case
• Next-to-leading order spin-orbit and spin(a)-spin(b) Hamiltonians for n gravitating spinning compact objects
• Canonical formulation of gravitating spinning objects at 3.5 post-Newtonian order
• Dressing the Post-Newtonian two-body problem and Classical Effective Field Theory
• Effective-one-body Hamiltonian with next-to-leading order spin-spin coupling for two nonprecessing black holes with aligned spins
• Elimination of the spin supplementary condition in the effective field theory approach to the post-Newtonian approximation
• Leading-order spin-orbit and spin(1)-spin(2) radiation-reaction Hamiltonians
• Theory of post-Newtonian radiation and reaction
• From the EFT of Spinning Gravitating Objects to Poincaré and Gauge Invariance at the 4.5PN Precision Frontier
• A nonlinear scalar model of extreme mass ratio inspirals in effective field theory I. Self force through third order
• Effective-one-body Hamiltonian with next-to-leading order spin-spin coupling
• Caged black hole thermodynamics: Charge, the extremal limit, and finite size effects
• Canonical Angles In A Compact Binary Star System With Spinning Components: Approximative Solution Through Next-To-Leading-Order Spin-Orbit Interaction for Circular Orbits
• Spin gauge symmetry in the action principle for classical relativistic particles
• Next-to-leading order spin-orbit effects in the equations of motion, energy loss and phase evolution of binaries of compact bodies in the effective field theory approach
• Gravitational radiation-reaction in arbitrary dimension
• Detweiler's redshift invariant for extended bodies orbiting a Schwarzschild black hole
• Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals
• Waveforms from Amplitudes
• Post-Newtonian Dynamics of Spinning Black Hole Binaries in Einstein-Scalar-Gauss-Bonnet Gravity
• A Post-Newtonian approach to black hole-fluid systems
• Binary dynamics from Einstein-Maxwell theory at second post-Newtonian order using effective field theory
• Classical Effective Field Theory for Weak Ultra Relativistic Scattering
• A public framework for Feynman calculations and post-Newtonian gravity
• Gravitational cubic-in-spin interaction at the next-to-leading post-Newtonian order
• Field theory for gravity at all scales
• Quantum point particle approximation of spinning black holes and compact stars