Built on

A. V. Smirnov and F. S. Chuharev, “FIRE6: Feynman Integral REduction with Modular Arithmetic,” Comput. Phys. Commun
Original
1901
Earlier work this paper cites.
Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng, “Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order,” Phys. Rev. Lett
Original
1901
Earlier work this paper cites.
S. Abreu, J. Dormans, F. Febres Cordero, H. Ita, B. Page, and V. Sotnikov, “Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD,” JHEP
Original
1904
Earlier work this paper cites.
Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng, “Black Hole Binary Dynamics from the Double Copy and Effective Theory,” JHEP
Original
1908
Earlier work this paper cites.
A. P. Saha, B. Sahoo, and A. Sen, “Proof of the classical soft graviton theorem in D D = 4,” JHEP
Original
1912
Earlier work this paper cites.
A. Einstein, “Über Gravitationswellen,” Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys. )
1918
Earlier work this paper cites.
H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, “Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems,” Proc. Roy. Soc. Lond. A
1962
Earlier work this paper cites.
R. K. Sachs, “Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times,” Proc. Roy. Soc. Lond. A
1962
Earlier work this paper cites.
S. Weinberg, “Infrared photons and gravitons,” Phys. Rev
1965
Earlier work this paper cites.
P. C. Peters, “Relativistic gravitational bremsstrahlung,” Phys. Rev. D
1970
Earlier work this paper cites.
M. J. Duff, “Quantum Tree Graphs and the Schwarzschild Solution,” Phys. Rev. D
1973
Earlier work this paper cites.
S. J. Kovacs and K. S. Thorne, “The Generation of Gravitational Waves. 3. Derivation of Bremsstrahlung Formulas,” Astrophys. J
1977
Earlier work this paper cites.
M. Portilla, “Scattering of Two Gravitating Particles: Classical Approach,” J. Phys. A
1980
Earlier work this paper cites.
K. G. Chetyrkin and F. V. Tkachov, “Integration by Parts: The Algorithm to Calculate beta Functions in 4 Loops,” Nucl. Phys. B
1981
Earlier work this paper cites.
T. Damour and N. Deruelle, “Radiation Reaction and Angular Momentum Loss in Small Angle Gravitational Scattering,” Phys. Lett. A
1981
Earlier work this paper cites.
L. Bel, T. Damour, N. Deruelle, J. Ibanez, and J. Martin, “Poincaré-invariant gravitational field and equations of motion of two pointlike objects: The postlinear approximation of general relativity,” Gen. Rel. Grav
1981
Earlier work this paper cites.
K. Westpfahl, “High-Speed Scattering of Charged and Uncharged Particles in General Relativity,” Fortsch. Phys
1985
Earlier work this paper cites.
T. Damour and N. Deruelle, “General relativistic celestial mechanics of binary systems. I. The post-Newtonian motion.,” Annales de L’Institut Henri Poincare Section (A) Physique Theorique
1985
Earlier work this paper cites.
L. Blanchet and T. Damour, “Radiative gravitational fields in general relativity I. general structure of the field outside the source,” Phil. Trans. Roy. Soc. Lond. A
1986
Earlier work this paper cites.
H. Kawai, D. C. Lewellen, and S. H. H. Tye, “A relation between tree amplitudes of closed and open strings,” Nucl. Phys
1986
Earlier work this paper cites.
T. Damour and G. Schaefer, “Higher Order Relativistic Periastron Advances and Binary Pulsars,” Nuovo Cim. B
1988
Earlier work this paper cites.
L. Blanchet and T. Damour, “Postnewtonian Generation of Gravitational Waves,” Ann. Inst. H. Poincare Phys. Theor
1989
Earlier work this paper cites.
A. V. Kotikov, “Differential equations method: New technique for massive Feynman diagrams calculation,” Phys. Lett. B
1991
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, “One loop n n -point gauge theory amplitudes, unitarity and collinear limits,” Nucl. Phys
1994
Earlier work this paper cites.
Z. Bern, L. J. Dixon, and D. A. Kosower, “Dimensionally regulated pentagon integrals,” Nucl. Phys. B
1994
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, “Fusing gauge theory tree amplitudes into loop amplitudes,” Nucl. Phys
1995
Earlier work this paper cites.
Z. Bern and A. G. Morgan, “Massive loop amplitudes from unitarity,” Nucl. Phys
1996
Earlier work this paper cites.
E. Remiddi, “Differential equations for Feynman graph amplitudes,” Nuovo Cim. A
1997
Earlier work this paper cites.
Z. Bern, L. J. Dixon, and D. A. Kosower, “One loop amplitudes for e+ e- to four partons,” Nucl. Phys. B
1998
Earlier work this paper cites.
M. Beneke and V. A. Smirnov, “Asymptotic expansion of Feynman integrals near threshold,” Nucl. Phys. B
1998
Earlier work this paper cites.

Similar

S. Laporta, “High precision calculation of multiloop Feynman integrals by difference equations,” Int. J. Mod. Phys. A
2000
Cited alongside, same era.
T. Gehrmann and E. Remiddi, “Differential equations for two loop four point functions,” Nucl. Phys. B
2000
Cited alongside, same era.
R. Britto, F. Cachazo, and B. Feng, “Generalized unitarity and one-loop amplitudes in N=4 super-Yang-Mills,” Nucl. Phys. B
2005
Cited alongside, same era.
L. Blanchet, “Energy losses by gravitational radiation in inspiraling compact binaries to five halves postNewtonian order,” Phys. Rev. D
2005
Cited alongside, same era.
J. Parra-Martinez, M. S. Ruf, and M. Zeng, “Extremal black hole scattering at 𝒪 ⁡ ( G 3 ) \mathcal{O}(G^{3}) : graviton dominance, eikonal exponentiation, and differential equations,” JHEP
Original
2005
Cited alongside, same era.

Then

G. U. Jakobsen, G. Mogull, J. Plefka, and J. Steinhoff, “Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory,” Phys. Rev. Lett
Original
2021
Later among the works it cites.
D. Bini, T. Damour, and A. Geralico, “Radiative contributions to gravitational scattering,” Phys. Rev. D
Original
2021
Later among the works it cites.
S. Mougiakakos, M. M. Riva, and F. Vernizzi, “Gravitational Bremsstrahlung in the post-Minkowskian effective field theory,” Phys. Rev. D
Original
2021
Later among the works it cites.
A. Cristofoli, R. Gonzo, D. A. Kosower, and D. O’Connell, “Waveforms from amplitudes,” Phys. Rev. D
Original
2022
Later among the works it cites.
Z. Bern, J. Parra-Martinez, R. Roiban, M. S. Ruf, C.-H. Shen, M. P. Solon, and M. Zeng, “Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at O(G4),” Phys. Rev. Lett

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2024

Gravitational Waveform: A Tale of Two Formalisms

Bini, Donato, Damour, Thibault, De Angelis, Stefano et al.

Understand

We revisit the quantum-amplitude-based derivation of the gravitational waveform emitted by the scattering of two spinless massive bodies at the third order in Newton's constant, $h \sim G+G^2+G^3$ (one-loop level), and correspondingly update its comparison with its classically-derived multipolar-post-Minkowskian counterpart.

A spurious-pole-free reorganization of the one-loop five-point amplitude substantially simplifies the post-Newtonian expansion.
We find complete agreement between the two results up to the fifth order in the small velocity expansion after taking into account three subtle aspects of the amplitude derivation: (1) in agreement with [arXiv:2312.07452 [hep-th]], the term quadratic in the amplitude in the observable-based formalism [JHEP 02, 137 (2019)] generates a frame rotation by half the classical scattering angle; (2) the dimensional regularization of the infrared divergences of the amplitude introduces an additional $(d-4)/(d-4)$ finite term; and (3) zero-frequency gravitons are found to contribute additional terms both at order $h \sim G^1$ and at order $h \sim G^3$ when including disconnected diagrams in the observable-based formalism.