Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Gravity Waves from Soft Theorem in General Dimensions

Alok Laddha, Ashoke Sen

TL;DR

This work shows that the classical limit of the multiple soft graviton theorem yields universal predictions for long-wavelength gravitational radiation in general dimensions, accessible either in the large-impact-parameter regime or the probe limit. It derives leading and subleading soft graviton factors, and when appropriate a subsubleading universal piece, and expresses the radiative field in terms of these factors, connecting directly to the angular power spectrum of emitted radiation. The authors test these predictions across diverse classical scattering scenarios (fusion/decay, multi-body scattering, and black-hole-related processes), and extend the analysis to soft photons, confirming known results and highlighting the structure of universal terms. They also discuss the modifications in four dimensions due to infrared divergences and situate the results in relation to memory effects and asymptotic symmetries, with implications for gravitational-wave phenomenology and multi-body dynamics.

Abstract

Classical limit of multiple soft graviton theorem can be used to compute the angular power spectrum of long wavelength gravitational radiation in classical scattering provided the total energy carried away by the radiation is small compared to the energies of the scatterers. We could ensure this either by taking the limit in which the impact parameter is large compared to the Schwarzschild radii of the scatterers, or by taking the probe limit where one object (the probe) has mass much smaller than the other object (the scatterer). We compute the results to subsubleading order in soft momentum and test them using explicit examples involving classical scattering. Our analysis also generalizes to the case where there are multiple objects involved in the scattering and the objects exchange mass, fragment or fuse into each other during the scattering. A similar analysis can be carried out for soft photons to subleading order, reproducing standard textbook results. We also discuss the modification of soft expansion in four dimensions beyond the leading order due to infrared divergences.

Gravity Waves from Soft Theorem in General Dimensions

TL;DR

This work shows that the classical limit of the multiple soft graviton theorem yields universal predictions for long-wavelength gravitational radiation in general dimensions, accessible either in the large-impact-parameter regime or the probe limit. It derives leading and subleading soft graviton factors, and when appropriate a subsubleading universal piece, and expresses the radiative field in terms of these factors, connecting directly to the angular power spectrum of emitted radiation. The authors test these predictions across diverse classical scattering scenarios (fusion/decay, multi-body scattering, and black-hole-related processes), and extend the analysis to soft photons, confirming known results and highlighting the structure of universal terms. They also discuss the modifications in four dimensions due to infrared divergences and situate the results in relation to memory effects and asymptotic symmetries, with implications for gravitational-wave phenomenology and multi-body dynamics.

Abstract

Classical limit of multiple soft graviton theorem can be used to compute the angular power spectrum of long wavelength gravitational radiation in classical scattering provided the total energy carried away by the radiation is small compared to the energies of the scatterers. We could ensure this either by taking the limit in which the impact parameter is large compared to the Schwarzschild radii of the scatterers, or by taking the probe limit where one object (the probe) has mass much smaller than the other object (the scatterer). We compute the results to subsubleading order in soft momentum and test them using explicit examples involving classical scattering. Our analysis also generalizes to the case where there are multiple objects involved in the scattering and the objects exchange mass, fragment or fuse into each other during the scattering. A similar analysis can be carried out for soft photons to subleading order, reproducing standard textbook results. We also discuss the modification of soft expansion in four dimensions beyond the leading order due to infrared divergences.

Paper Structure

This paper contains 21 sections, 192 equations, 2 figures.

Table of Contents

  1. Introduction and summary
  2. Electromagnetic radiation from classical scattering
  3. Gravitational radiation from classical scattering
  4. Sum over polarizations for probe scattering
  5. Plunge
  6. Universal parts of higher order non-universal results
  7. Subleading soft photon theorem
  8. Subsubleading soft graviton theorem
  9. Hidden assumptions
  10. Tests of soft theorem from classical radiation analysis
  11. Soft photon theorem
  12. Soft graviton theorem
  13. Scattering via fusion and decay:
  14. Scattering via multiple fusion and decay
  15. Inclusion of spin
  16. ...and 6 more sections

Figures (2)

  • Figure 1: A scattering process in space-time.
  • Figure 2: A more complicated scattering process in space-time.