open access publication

Article, 2023

Radiation Reaction and Gravitational Waves at Fourth Post-Minkowskian Order

In: Physical Review Letters, ISSN 0031-9007, 1079-7114, Volume 130, 10, Page 101401, 10.1103/physrevlett.130.101401

Contributors (5)

Dlapa, Christoph (0000-0003-4336-3170) [1] Kälin, Gregor (0000-0002-6697-775X) [1] Liu, Zhengwen (0000-0002-2628-9063) [1] [2] Neef, Jakob [3] [4] Porto, Rafael A (0000-0003-0129-1930) [1]


  1. [1] Deutsches Elektronen-Synchrotron DESY
  2. [NORA names: Germany; Europe, EU; OECD]
  3. [2] University of Copenhagen
  4. [NORA names: KU University of Copenhagen; University; Denmark; Europe, EU; Nordic; OECD]
  5. [3] Humboldt-Universität zu Berlin
  6. [NORA names: Germany; Europe, EU; OECD]
  7. [4] University College Dublin
  8. [NORA names: Ireland; Europe, EU; OECD]


We obtain the total impulse in the scattering of nonspinning binaries in general relativity at fourth post-Minkowskian order, i.e., O(G^{4}), including linear, nonlinear, and hereditary radiation-reaction effects. We derive the total radiated spacetime momentum as well as the associated energy flux. The latter can be used to compute gravitational-wave observables for generic (un)bound orbits. We employ the ("in-in") Schwinger-Keldysh worldline effective field theory framework in combination with modern "multiloop" integration techniques from collider physics. The complete results are in agreement with various partial calculations in the post-Minkowskian and post-Newtonian expansion.


agreement, associated energy fluxes, binaries, calculations, collider physics, combination, complete results, effect, effective field theory framework, energy flux, expansion, field theory framework, flux, framework, general relativity, gravitational wave observables, gravitational waves, impulses, integration technique, latter, momentum, multiloop, observables, orbit, order, partial calculation, physics, post-Minkowskian order, post-Newtonian expansion, radiation reaction, radiation reaction effects, reaction, relativity, results, scattering, technique, theory framework, total impulse, waves


  • Danish Agency for Science and Higher Education
  • European Research Council
  • Deutsche Forschungsgemeinschaft
  • Carlsberg Foundation
  • Directorate for Mathematical & Physical Sciences
  • European Commission