Hamiltonian for tidal interactions in compact binary systems to next-to-next-to-leading post-Newtonian order

Abstract

In previous works, we obtained the leading, next-to-leading and next-to-next-to-leading (NNL) post-Newtonian (PN) corrections in the conservative tidal interactions between two compact non-spinning objects using a Lagrangian of effective field theory (EFT) in harmonic coordinates. In the present paper, we compute the corresponding NNL PN tidal effective Hamiltonian in ADM-like and isotropic coordinates, with contributions from mass quadrupole, current quadrupole and mass octupole tidal interactions, consistently included at that level. We also derive the NNL tidal Hamiltonian in Delaunay variables. We find full agreement in the overlap with recent results that were derived using tools from scattering amplitudes and the EFT to second post-Minkowskian (PM) order.

arXiv comment10 pages

References in corpus (31)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• GW190425: Observation of a Compact Binary Coalescence with Total Mass $\sim 3.4M_{\odot }$
• Tidal Love numbers of neutron stars
• Constraining neutron star tidal Love numbers with gravitational wave detectors
• Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral
• Relativistic tidal properties of neutron stars
• Relativistic theory of tidal Love numbers
• An Effective Field Theory of Gravity for Extended Objects
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Measurability of the tidal polarizability of neutron stars in late-inspiral gravitational-wave signals
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• Systematic parameter errors in inspiraling neutron star binaries
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• High-energy gravitational scattering and the general relativistic two-body problem
• General Relativity from Scattering Amplitudes
• Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics
• Third post-Newtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic-coordinate and ADM-Hamiltonian formalisms
• General relativistic dynamics of compact binaries at the third post-Newtonian order
• Fourth post-Newtonian effective one-body dynamics
• Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order
• Effective action approach to higher-order relativistic tidal interactions in binary systems and their effective one body description
• Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation
• On the multipole expansion of the gravitational field
• Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order
• Tidal Effects in the Post-Minkowskian Expansion
• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
• Derivation of local-in-time fourth post-Newtonian ADM Hamiltonian for spinless compact binaries
• Tidal effects in the gravitational-wave phase evolution of compact binary systems to next-to-next-to-leading post-Newtonian order
• Tidal effects in the equations of motion of compact binary systems to next-to-next-to-leading post-Newtonian order
• Equations of motion of self-gravitating $N$-body systems in the first post-Minkowskian approximation

Cited by in corpus (10)

• Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• The Science of the Einstein Telescope
• Gravitational Wave Flux and Quadrupole Modes from Quasi-Circular Non-Spinning Compact Binaries to the Fourth Post-Newtonian Order
• Spin effects on neutron star fundamental-mode dynamical tides: phenomenology and comparison to numerical simulations
• Gravitational Bremsstrahlung with tidal effects in the post-Minkowskian expansion
• Relativistic effective action of dynamical gravitomagnetic tides for slowly rotating neutron stars
• Angular Momentum Loss Due to Tidal Effects in the Post-Minkowskian Expansion
• Waveforms from Amplitudes
• Tidal contributions to the full gravitational waveform to the second-and-a-half post-Newtonian order