Renormalizing Love: tidal effects at the third post-Newtonian order

Abstract

We present the conservative effective two-body Hamiltonian at the third order in the post-Newtonian expansion with gravitoelectric quadrupolar dynamical tidal-interactions. Our derivation of the effective two-body Lagrangian is based on the diagrammatic effective field theory approach and it involves Feynman integrals up to three loops, which are evaluated within the dimensional regularization scheme. The elimination of the divergent terms occurring in the effective Lagrangian requires the addition of counterterms to ensure finite observables, thereby introducing a renormalization group flow to the post-adiabatic Love number. As a limiting case of the renormalized dynamical effective Hamiltonian, we also derive the effective Hamiltonian for adiabatic tides, and, in this regime, calculate the binding energy for a circular orbit, and the scattering angle in a hyperbolic scattering.

27 pages, 3 figures, 1 table; matches the published version. arXiv admin note: text overlap with arXiv:2304.02030

References in corpus (23)

• Advanced LIGO
• Tidal Love numbers of neutron stars
• Constraining neutron star tidal Love numbers with gravitational wave detectors
• Relativistic theory of tidal Love numbers
• Post-1-Newtonian tidal effects in the gravitational waveform from binary inspirals
• Dynamical Tides in General Relativity: Effective Action and Effective-One-Body Hamiltonian
• Tidal effects in binary neutron star coalescence
• Non-Relativistic Gravitation: From Newton to Einstein and Back
• Gravitational self-force corrections to two-body tidal interactions and the effective one-body formalism
• Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals
• Classical Effective Field Theory and Caged Black Holes
• Effective-one-body multipolar waveform for tidally interacting binary neutron stars up to merger
• Gravitational scattering of two black holes at the fourth post-Newtonian approximation
• Resonant Tidal Excitation of Oscillation Modes in Merging Binary Neutron Stars: Inertial-Gravity Modes
• Scattering of tidally interacting bodies in post-Minkowskian gravity
• Gravitomagnetic response of an irrotational body to an applied tidal field
• Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model
• Non-linearities in the tidal Love numbers of black holes
• Gravitomagnetic Love tensor of a slowly rotating body: post-Newtonian theory
• Impact of the tidal p-g instability on the gravitational wave signal from coalescing binary neutron stars
• Relativistic effective action of dynamical gravitomagnetic tides for slowly rotating neutron stars
• Addressing issues in defining the Love numbers for black holes
• Gravitoelectric dynamical tides at second post-Newtonian order

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• Rotating black holes experience dynamical tides
• Cost of inferred nuclear parameters towards the f-mode dynamical tide in binary neutron stars
• Radiating Love: adiabatic tidal fluxes and modes up to next-to-next-to-leading post-Newtonian order
• Tidal contributions to the full gravitational waveform to the second-and-a-half post-Newtonian order
• Modeling matter(s) in SEOBNRv5THM: Generating fast and accurate effective-one-body waveforms for spin-aligned binary neutron stars
• Dynamical Tidal Response of Non-rotating Black Holes: Connecting the MST Formalism and Worldline EFT
• Dynamical Love Numbers for Black Holes and Beyond from Shell Effective Field Theory
• High-order effective-one-body tidal interactions and gravitational scattering
• On the logarithmic Love number of black holes beyond general relativity