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Horizon radiation reaction forces

Walter D. Goldberger, Ira Z. Rothstein

TL;DR

This work addresses horizon dissipation in the dynamics of binary black holes and its imprint on gravitational interactions. It develops a model-independent EFT framework that uses worldline internal degrees of freedom and the In-In formalism to treat real-time dissipation, in both post-Minkowskian and post-Newtonian regimes. It reports concrete results: in PM scattering it yields inelastic momentum transfer and a final mass distribution consistent with the area theorem and provides corrections to the CM scattering angle; in PN dynamics it derives a 6.5PN damping force and the associated instantaneous energy and angular momentum losses due to horizon absorption. The approach is readily generalizable to other compact objects and has potential applications to gravitational-wave templates that encode horizon physics.

Abstract

Using Effective Field Theory (EFT) methods, we compute the effects of horizon dissipation on the gravitational interactions of relativistic binary black hole systems. We assume that the dynamics is perturbative, i.e it admits an expansion in powers of Newton's constant (post-Minkowskian, or PM, approximation). As applications, we compute corrections to the scattering angle in a black hole collision due to dissipative effects to leading PM order, as well as the post-Newtonian (PN) corrections to the equations of motion of binary black holes in non-relativistic orbits, which represents the leading order finite size effect in the equations of motion. The methods developed here are also applicable to the case of more general compact objects, eg. neutron stars, where the magnitude of the dissipative effects depends on non-gravitational physics (e.g, the equation of state for nuclear matter).

Horizon radiation reaction forces

TL;DR

This work addresses horizon dissipation in the dynamics of binary black holes and its imprint on gravitational interactions. It develops a model-independent EFT framework that uses worldline internal degrees of freedom and the In-In formalism to treat real-time dissipation, in both post-Minkowskian and post-Newtonian regimes. It reports concrete results: in PM scattering it yields inelastic momentum transfer and a final mass distribution consistent with the area theorem and provides corrections to the CM scattering angle; in PN dynamics it derives a 6.5PN damping force and the associated instantaneous energy and angular momentum losses due to horizon absorption. The approach is readily generalizable to other compact objects and has potential applications to gravitational-wave templates that encode horizon physics.

Abstract

Using Effective Field Theory (EFT) methods, we compute the effects of horizon dissipation on the gravitational interactions of relativistic binary black hole systems. We assume that the dynamics is perturbative, i.e it admits an expansion in powers of Newton's constant (post-Minkowskian, or PM, approximation). As applications, we compute corrections to the scattering angle in a black hole collision due to dissipative effects to leading PM order, as well as the post-Newtonian (PN) corrections to the equations of motion of binary black holes in non-relativistic orbits, which represents the leading order finite size effect in the equations of motion. The methods developed here are also applicable to the case of more general compact objects, eg. neutron stars, where the magnitude of the dissipative effects depends on non-gravitational physics (e.g, the equation of state for nuclear matter).

Paper Structure

This paper contains 7 sections, 45 equations, 1 figure.

Table of Contents

  1. Introduction
  2. In-In formalism for black hole dissipative forces
  3. Horizon dissipation in dynamical gravity
  4. Inelastic BH-BH scattering in the PM approximation
  5. Post-Newtonian equations of motion for binary dynamics
  6. Conclusions
  7. Acknowledgments

Figures (1)

  • Figure 1: Potential exchange diagrams that contribute to the two-particle action $S_{int}$. In (a) the particles interact through the minimal gravitational interaction. Figure (b) is the term in $S_{int}$ generated by the quadrupole couplings of particle 1 (a similar diagram with $1\leftrightarrow 2$ has been omitted).