The Lamb shift and the gravitational binding energy for binary black holes

Abstract

We show that the correction to the gravitational binding energy for binary black holes due to the tail effect resembles the Lamb shift in the Hydrogen atom. In both cases a 'conservative' effect arises from interactions with 'radiation' modes, and moreover an explicit cancelation between near and far zone divergences is at work. In addition, regularization scheme-dependence may introduce ambiguity parameters. This is remediated, within an effective field theory approach, by the implementation of the zero-bin subtraction. We illustrate the procedure explicitly for the Lamb shift, by performing an ambiguity-free derivation within the framework of non-relativistic electrodynamics. We also derive the renormalization group equations from which we reproduce Bethe logarithm (at order ${\alpha }_e^5\log {\alpha }_e$), and likewise the contribution to the gravitational potential from the tail effect (proportional to $v^8\log v$).

18 pages. 6 figures. To appear in Phys. Rev. D

References in corpus (16)

• The Zero-Bin and Mode Factorization in Quantum Field Theory
• Testing strong-field gravity with tidal Love numbers
• The Hyperfine Einstein-Infeld-Hoffmann Potential
• High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry
• Effective field theory approach to the gravitational two-body dynamics, at fourth post-Newtonian order and quintic in the Newton constant
• The Tune of Love and the Nature(ness) of Spacetime
• Effective field theory calculation of second post-Newtonian binary dynamics
• Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order
• The dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant
• Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order
• The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
• On the Apparent Ambiguities in the Post-Newtonian Expansion for Binary Systems
• TASI Lectures on Effective Field Theories
• Les Houches Lectures on Effective Field Theories and Gravitational Radiation
• On the four-loop static contribution to the gravitational interaction potential of two point masses
• First Law of Compact Binary Mechanics with Gravitational-Wave Tails

Cited by in corpus (23)

• Amplitudes, Observables, and Classical Scattering
• Probing Ultralight Bosons with Binary Black Holes
• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
• From Boundary Data to Bound States
• Dynamics of Binary Systems to Fourth Post-Minkowskian Order from the Effective Field Theory Approach
• From Boundary Data to Bound States II: Scattering Angle to Dynamical Invariants (with Twist)
• Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian
• Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• From amplitudes to gravitational radiation with cubic interactions and tidal effects
• On the Apparent Ambiguities in the Post-Newtonian Expansion for Binary Systems
• Gravitational radiation from inspiralling compact objects: Spin effects to fourth Post-Newtonian order
• Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order
• Resummed spinning waveforms from five-point amplitudes
• Radiation reaction for spinning bodies in effective field theory II: Spin-spin effects
• Hereditary Terms at Next-To-Leading Order in Two-Body Gravitational Dynamics
• Radiation reaction for spinning bodies in effective field theory I: Spin-orbit effects
• Trace anomaly contribution to hydrogen atom mass
• Machine Learning Post-Minkowskian Integrals
• Classical gravitational scattering from a gauge-invariant double copy