Abstract
Classical soft graviton theorem gives the gravitational wave-form at future null infinity at late retarded time u for a general classical scattering. The large u expansion has three known universal terms: the constant term, the term proportional to 1/u and the term proportional to ln u/u2, whose coefficients are determined solely in terms of the momenta of incoming and the outgoing hard particles, including the momenta carried by outgoing gravitational and electromagnetic radiation produced during scattering. For the constant term, also known as the memory effect, the dependence on the momenta carried away by the final state radiation / massless particles is known as non-linear memory or null memory. It was shown earlier that for the coefficient of the 1/u term the dependence on the momenta of the final state massless particles / radiation cancels and the result can be written solely in terms of the momenta of the incoming particles / radiation and the final state massive particles. In this note we show that the same result holds for the coefficient of the ln u/u2 term. Our result implies that for scattering of massless particles the coefficients of the 1/u and ln u/u2 terms are determined solely by the incoming momenta, even if the particles coalesce to form a black hole and massless radiation. We use our result to compute the low frequency flux of gravitational radiation from the collision of massless particles at large impact parameter.
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References
A. Laddha and A. Sen, Observational signature of the logarithmic terms in the soft graviton theorem, Phys. Rev. D 100 (2019) 024009 [arXiv:1806.01872] [INSPIRE].
B. Sahoo and A. Sen, Classical and quantum results on logarithmic terms in the soft theorem in four dimensions, JHEP 02 (2019) 086 [arXiv:1808.03288] [INSPIRE].
A.P. Saha, B. Sahoo and A. Sen, Proof of the classical soft graviton theorem in D = 4, JHEP 06 (2020) 153 [arXiv:1912.06413] [INSPIRE].
B. Sahoo, Classical sub-subleading soft photon and soft graviton theorems in four spacetime dimensions, JHEP 12 (2020) 070 [arXiv:2008.04376] [INSPIRE].
Y.B. Zel’dovich and A.G. Polnarev, Radiation of gravitational waves by a cluster of superdense stars, Sov. Astron. 18 (1974) 17 [INSPIRE].
V.B. Braginsky and L.P. Grishchuk, Kinematic resonance and memory effect in free mass gravitational antennas, Sov. Phys. JETP 62 (1985) 427 [Zh. Eksp. Teor. Fiz. 89 (1985) 744] [INSPIRE].
V.B. Braginsky and K.S. Thorne, Gravitational-wave bursts with memory and experimental prospects, Nature 327 (1987) 123.
M. Ludvigsen, Geodesic deviation at null infinity and the physical effects of very long wave gravitational radiation, Gen. Rel. Grav. 21 (1989) 1205 [INSPIRE].
D. Christodoulou, Nonlinear nature of gravitation and gravitational wave experiments, Phys. Rev. Lett. 67 (1991) 1486 [INSPIRE].
K.S. Thorne, Gravitational-wave bursts with memory: the Christodoulou effect, Phys. Rev. D 45 (1992) 520 [INSPIRE].
L. Blanchet and T. Damour, Hereditary effects in gravitational radiation, Phys. Rev. D 46 (1992) 4304 [INSPIRE].
M. Favata, The gravitational-wave memory effect, Class. Quant. Grav. 27 (2010) 084036 [arXiv:1003.3486] [INSPIRE].
A. Tolish and R.M. Wald, Retarded fields of null particles and the memory effect, Phys. Rev. D 89 (2014) 064008 [arXiv:1401.5831] [INSPIRE].
L. Bieri and D. Garfinkle, Perturbative and gauge invariant treatment of gravitational wave memory, Phys. Rev. D 89 (2014) 084039 [arXiv:1312.6871] [INSPIRE].
A. Strominger and A. Zhiboedov, Gravitational memory, BMS supertranslations and soft theorems, JHEP 01 (2016) 086 [arXiv:1411.5745] [INSPIRE].
A. Gruzinov and G. Veneziano, Gravitational radiation from massless particle collisions, Class. Quant. Grav. 33 (2016) 125012 [arXiv:1409.4555] [INSPIRE].
M. Ciafaloni, D. Colferai and G. Veneziano, Infrared features of gravitational scattering and radiation in the eikonal approach, Phys. Rev. D 99 (2019) 066008 [arXiv:1812.08137] [INSPIRE].
A. Addazi, M. Bianchi and G. Veneziano, Soft gravitational radiation from ultra-relativistic collisions at sub- and sub-sub-leading order, JHEP 05 (2019) 050 [arXiv:1901.10986] [INSPIRE].
A. Laddha and A. Sen, Gravity waves from soft theorem in general dimensions, JHEP 09 (2018) 105 [arXiv:1801.07719] [INSPIRE].
D. Amati, M. Ciafaloni and G. Veneziano, Superstring collisions at Planckian energies, Phys. Lett. B 197 (1987) 81 [INSPIRE].
D. Ghosh and B. Sahoo, Spin dependent gravitational tail memory in D = 4, arXiv:2106.10741 [INSPIRE].
M. Campiglia and A. Laddha, Loop corrected soft photon theorem as a Ward identity, JHEP 10 (2019) 287 [arXiv:1903.09133] [INSPIRE].
S. Atul Bhatkar, Ward identity for loop level soft photon theorem for massless QED coupled to gravity, JHEP 10 (2020) 110 [arXiv:1912.10229] [INSPIRE].
S. Atul Bhatkar, New asymptotic conservation laws forelectromagnetism, JHEP 02 (2021) 082 [arXiv:2007.03627] [INSPIRE].
S. Atul Bhatkar, Asymptotic conservation law with Feynman boundary condition, Phys. Rev. D 103 (2021) 125026 [arXiv:2101.09734] [INSPIRE].
R.H. Price, Nonspherical perturbations of relativistic gravitational collapse. 1. Scalar and gravitational perturbations, Phys. Rev. D 5 (1972) 2419 [INSPIRE].
R.H. Price, Nonspherical perturbations of relativistic gravitational collapse. Part II. Integer-spin, zero-rest-mass fields, Phys. Rev. D 5 (1972) 2439 [INSPIRE].
S. Ma and L. Zhang, Price’s law for spin fields on a Schwarzschild background, arXiv:2104.13809 [INSPIRE].
C. Gundlach, R.H. Price and J. Pullin, Late time behavior of stellar collapse and explosions: 1. Linearized perturbations, Phys. Rev. D 49 (1994) 883 [gr-qc/9307009] [INSPIRE].
C. Gundlach, R.H. Price and J. Pullin, Late time behavior of stellar collapse and explosions: 2. Nonlinear evolution, Phys. Rev. D 49 (1994) 890 [gr-qc/9307010] [INSPIRE].
E.W. Leaver, Spectral decomposition of the perturbation response of the Schwarzschild geometry, Phys. Rev. D 34 (1986) 384 [INSPIRE].
M. Dafermos and I. Rodnianski, A proof of Price’s law for the collapse of a selfgravitating scalar field, Invent. Math. 162 (2005) 381 [gr-qc/0309115] [INSPIRE].
Y. Angelopoulos, S. Aretakis and D. Gajic, Logarithmic corrections in the asymptotic expansion for the radiation field along null infinity, J. Hyperbol. Diff. Equat. 16 (2019) 1 [arXiv:1712.09977] [INSPIRE].
L.M.A. Kehrberger, The case against smooth null infinity II: a logarithmically modified price’s law, arXiv:2105.08084 [INSPIRE].
L.M.A. Kehrberger, The case against smooth null infinity III: early-time asymptotics for higher ℓ-modes of linear waves on a Schwarzschild background, arXiv:2106.00035 [INSPIRE].
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Sahoo, B., Sen, A. Classical soft graviton theorem rewritten. J. High Energ. Phys. 2022, 77 (2022). https://doi.org/10.1007/JHEP01(2022)077
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DOI: https://doi.org/10.1007/JHEP01(2022)077