Gravitational self-force in the ultra-relativistic limit: The 'large-N' expansion

Abstract

We study the gravitational self-force using the effective field theory formalism. We show that in the ultra-relativistic limit γ\to \infty, with γthe boost factor, many simplifications arise. Drawing parallels with the large N limit in quantum field theory, we introduce the parameter 1/N = 1/γ^2 and show that the effective action admits a well defined expansion in powers of λ= Nε, at each order in 1/N, where ε= E_m/M and E_m=γm is the (kinetic) energy of the small mass. Moreover, we show that diagrams with nonlinear bulk interactions first enter at O(λ^2/N^2) and only diagrams with nonlinearities in the worldline couplings, which are significantly easier to compute, survive in the large N/ultra-relativistic limit. Finally, we derive the self-force to O(λ^4/N) and provide expressions for some conservative quantities for circular orbits.

12+23 pages, 24 figures. Paper substantially extended with more details on the formalism and computations. Submitted to JHEP

References in corpus (15)

• The Effective Field Theory of Inflation
• Effective Field Theory for Inflation
• The classical mechanics of non-conservative systems
• The Hyperfine Einstein-Infeld-Hoffmann Potential
• Viscosity and dissipative hydrodynamics from effective field theory
• Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring
• Effective field theory calculation of second post-Newtonian binary dynamics
• The quantum mechanics of perfect fluids
• 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
• Dissipation in the effective field theory for hydrodynamics: First order effects
• Self-force on extreme mass ratio inspirals via curved spacetime effective field theory
• Black hole mass dynamics and renormalization group evolution
• Electromagnetic and gravitational self-force on a relativistic particle from quantum fields in curved space
• Caustic echoes from a Schwarzschild black hole

Cited by in corpus (26)

• Amplitudes, Observables, and Classical Scattering
• The Effective Field Theorist's Approach to Gravitational Dynamics
• Self-force and radiation reaction in general relativity
• Probing Ultralight Bosons with Binary Black Holes
• Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics
• 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
• Radiation and the classical double copy for color charges
• From Boundary Data to Bound States
• 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
• The Tune of Love and the Nature(ness) of Spacetime
• Gravitational Bremsstrahlung in the Post-Minkowskian Effective Field Theory
• Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
• Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics
• Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
• Gravitational Bremsstrahlung with tidal effects in the post-Minkowskian expansion
• Self-force via Green functions and worldline integration
• All order gravitational waveforms from scattering amplitudes
• Black Hole Formation from the Collision of Plane-Fronted Gravitational Waves
• A scattering theory of ultrarelativistic solitons
• Analytic approximations, perturbation theory, effective field theory methods and their applications
• Can Two Ultrarelativistic Objects Lose Almost All Their Energy to Gravitational Radiation?
• Half-solution to the two-body problem in General Relativity
• Testing gravity with the two-body problem