An Effective Field Theory of Gravity for Extended Objects

Abstract

We present an Effective Field Theory (EFT) formalism which describes the dynamics of non-relativistic extended objects coupled to gravity. The formalism is relevant to understanding the gravitational radiation power spectra emitted by binary star systems, an important class of candidate signals for gravitational wave observatories such as LIGO or VIRGO. The EFT allows for a clean separation of the three relevant scales: r_s, the size of the compact objects, r the orbital radius and r/v, the wavelength of the physical radiation (where the velocity v is the expansion parameter). In the EFT radiation is systematically included in the v expansion without need to separate integrals into near zones and radiation zones. We show that the renormalization of ultraviolet divergences which arise at v^6 in post-Newtonian (PN) calculations requires the presence of two non-minimal worldline gravitational couplings linear in the Ricci curvature. However, these operators can be removed by a redefinition of the metric tensor, so that the divergences at arising at v^6 have no physically observable effect. Because in the EFT finite size features are encoded in the coefficients of non-minimal couplings, this implies a simple proof of the decoupling of internal structure for spinless objects to at least order v^6. Neglecting absorptive effects, we find that the power counting rules of the EFT indicate that the next set of short distance operators, which are quadratic in the curvature and are associated with tidal deformations, do not play a role until order v^10. These operators, which encapsulate finite size properties of the sources, have coefficients that can be fixed by a matching calculation. By including the most general set of such operators, the EFT allows one to work within a point particle theory to arbitrary orders in v.

LaTeX 24 pages, 11 figures. Added discussion of field redefinitions. New appendix with Feynman rules

References in corpus (2)

• Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order
• Dimensional regularization of the third post-Newtonian gravitational wave generation from two point masses

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• Classical Effective Field Theory for Weak Ultra Relativistic Scattering
• Tidal Love Numbers of Neutron Stars in Horndeski Theories
• A study of non-linear Langevin dynamics under non-Gaussian noise with quartic cumulant
• Black Hole and Neutron Star Binaries: Theoretical Challenges
• Gravitational cubic-in-spin interaction at the next-to-leading post-Newtonian order
• A public framework for Feynman calculations and post-Newtonian gravity
• Comments on initial conditions for the Abraham-Lorentz(-Dirac) equation
• Love beyond Einstein: Metric reconstruction and Love number in quadratic gravity using WEFT
• Classical Dimensional Transmutation and Renormalization in Massive lambda phi^4 Model
• Dynamical Love Numbers for Black Holes and Beyond from Shell Effective Field Theory
• Leading anomalies, the drift Hamiltonian and the relativistic two-body system
• Pseudo-topological Quasi-local Energy of Torsion Gravity
• Quantum gravity phenomenology from the perspective of quantum general relativity and quadratic gravity
• On-shell approach to scalar hair in spinning binaries
• Relativistic single-electron wavepacket in quantum electromagnetic fields: Quantum coherence, correlations, and the Unruh effect
• Resummed energy loss in extreme-mass-ratio scattering using critical orbits
• Caged black hole with Maxwell charge
• High-order effective-one-body tidal interactions and gravitational scattering
• A supplementary radiation-reaction force between two binaries
• Highest-weight truncation, graded EFT structure, and renormalization of black hole Love numbers
• Non-relativistic Effective Quantum Mechanics of the Coulomb Interaction
• Limits on the anomalous speed of gravitational waves from binary pulsars
• First-post-Newtonian generation of gravitational waves in Einstein-Cartan theory
• Quantum point particle approximation of spinning black holes and compact stars
• Double soft graviton factors from the gravitational Wilson line
• The Radial Action from Probe Amplitudes to All Orders
• Tidal effects in the total flux and waveform in massless scalar-tensor theories to, respectively, relative 2PN and 1.5PN orders
• First post-Newtonian correction to gravitational waves produced by compact binaries: How to compute relativistic corrections to gravitational waves using Feynman diagrams
• Exploring gravitational impulse via quantum Boltzmann equation
• Gravitational Wave Signals from Finite Size Effects in Spinning Binary Inspirals Including Parity Violating Constituents
• Field theory for gravity at all scales
• Equivalence Principle on Cosmological Backgrounds in Scalar-Tensor Theories
• On the EFT of Dyon-Monopole Catalysis
• Anomalous curvature evolution and geometric regularization of energy focusing in the snapping dynamics of a flexible body
• Quantum Corrections to Gravitational Potential of Scalarized Neutron Star Binary
• Influence Through Mixing: Hotspots as Benchmarks for Basic Black-Hole Behaviour
• Extremely High-Order Convergence in Simulations of Relativistic Stars
• The Fields of Ultra-Relativistic Gravitation
• Effective-one-body formalism for leading-order radiative effects in the post-linear framework
• Calculating the static gravitational two-body potential to fifth post-Newtonian order with Feynman diagrams
• Graviton Photoproduction by a Kerr-Newman Black Hole with Worldline EFT
• Lorentz from Galilei, deductively
• Hamiltonian normal forms for the post-Newtonian binary problem
• Worldline EFT treatment of quadratic and cubic gravity theories
• Trails of clouds in binary black holes
• Testing gravity with the two-body problem
• Some aspects of CP violation and gauge interactions in the standard model and beyond
• On the logarithmic Love number of black holes beyond general relativity
• Newman-Janis Algorithm from Taub-NUT Instantons
• Extremal Love: tidal/electromagnetic deformability, logarithmic running and the weak gravity conjecture
• Entire Four-Graviton EFT from the Duality Between Color and Kinematics
• 1PN effective binary Lagrangian for the gravity-Kalb-Ramond sector in the conservative regime
• General Relativity from Quantum Field Theory