Abstract
A characteristic value formulation of the Weyl double copy leads to an asymptotic formulation. We find that the Weyl double copy holds asymptotically in cases where the full solution is algebraically general, using rotating STU supergravity black holes as an example. The asymptotic formulation provides clues regarding the relation between asymptotic symmetries that follows from the double copy. Using the C-metric as an example, we show that a previous interpretation of this gravity solution as a superrotation has a single copy analogue relating the appropriate Liénard-Wiechert potential to a large gauge transformation.
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Z. Bern, J.J. Carrasco, M. Chiodaroli, H. Johansson and R. Roiban, The Duality Between Color and Kinematics and its Applications, arXiv:1909.01358 [INSPIRE].
H. Kawai, D.C. Lewellen and S.H.H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476] [INSPIRE].
R. Monteiro, D. O’Connell and C.D. White, Black holes and the double copy, JHEP 12 (2014) 056 [arXiv:1410.0239] [INSPIRE].
A. Luna, R. Monteiro, D. O’Connell and C.D. White, The classical double copy for Taub-NUT spacetime, Phys. Lett. B 750 (2015) 272 [arXiv:1507.01869] [INSPIRE].
A. Luna, R. Monteiro, I. Nicholson and D. O’Connell, Type D Spacetimes and the Weyl Double Copy, Class. Quant. Grav. 36 (2019) 065003 [arXiv:1810.08183] [INSPIRE].
H. Godazgar, M. Godazgar, R. Monteiro, D. Peinador Veiga and C.N. Pope, Weyl Double Copy for Gravitational Waves, Phys. Rev. Lett. 126 (2021) 101103 [arXiv:2010.02925] [INSPIRE].
A. Luna, R. Monteiro, I. Nicholson, D. O’Connell and C.D. White, The double copy: Bremsstrahlung and accelerating black holes, JHEP 06 (2016) 023 [arXiv:1603.05737] [INSPIRE].
W.D. Goldberger and A.K. Ridgway, Radiation and the classical double copy for color charges, Phys. Rev. D 95 (2017) 125010 [arXiv:1611.03493] [INSPIRE].
A. Luna et al., Perturbative spacetimes from Yang-Mills theory, JHEP 04 (2017) 069 [arXiv:1611.07508] [INSPIRE].
N. Arkani-Hamed, Y.-t. Huang and D. O’Connell, Kerr black holes as elementary particles, JHEP 01 (2020) 046 [arXiv:1906.10100] [INSPIRE].
Y.-T. Huang, U. Kol and D. O’Connell, Double copy of electric-magnetic duality, Phys. Rev. D 102 (2020) 046005 [arXiv:1911.06318] [INSPIRE].
K. Kim, K. Lee, R. Monteiro, I. Nicholson and D. Peinador Veiga, The Classical Double Copy of a Point Charge, JHEP 02 (2020) 046 [arXiv:1912.02177] [INSPIRE].
A. Luna, S. Nagy and C. White, The convolutional double copy: a case study with a point, JHEP 09 (2020) 062 [arXiv:2004.11254] [INSPIRE].
A. Cristofoli, Gravitational shock waves and scattering amplitudes, JHEP 11 (2020) 160 [arXiv:2006.08283] [INSPIRE].
R. Monteiro, D. O’Connell, D. Peinador Veiga and M. Sergola, Classical solutions and their double copy in split signature, JHEP 05 (2021) 268 [arXiv:2012.11190] [INSPIRE].
A. Guevara, B. Maybee, A. Ochirov, D. O’connell and J. Vines, A worldsheet for Kerr, JHEP 03 (2021) 201 [arXiv:2012.11570] [INSPIRE].
D.A. Kosower, B. Maybee and D. O’Connell, Amplitudes, Observables, and Classical Scattering, JHEP 02 (2019) 137 [arXiv:1811.10950] [INSPIRE].
C.D. White, Twistorial Foundation for the Classical Double Copy, Phys. Rev. Lett. 126 (2021) 061602 [arXiv:2012.02479] [INSPIRE].
E. Chacón, S. Nagy and C.D. White, The Weyl double copy from twistor space, JHEP 05 (2021) 2239 [arXiv:2103.16441] [INSPIRE].
J.F. Plebanski and M. Demianski, Rotating, charged, and uniformly accelerating mass in general relativity, Annals Phys. 98 (1976) 98 [INSPIRE].
A.K. Ridgway and M.B. Wise, Static Spherically Symmetric Kerr-Schild Metrics and Implications for the Classical Double Copy, Phys. Rev. D 94 (2016) 044023 [arXiv:1512.02243] [INSPIRE].
C.D. White, Exact solutions for the biadjoint scalar field, Phys. Lett. B 763 (2016) 365 [arXiv:1606.04724] [INSPIRE].
W.D. Goldberger, S.G. Prabhu and J.O. Thompson, Classical gluon and graviton radiation from the bi-adjoint scalar double copy, Phys. Rev. D 96 (2017) 065009 [arXiv:1705.09263] [INSPIRE].
T. Adamo, E. Casali, L. Mason and S. Nekovar, Scattering on plane waves and the double copy, Class. Quant. Grav. 35 (2018) 015004 [arXiv:1706.08925] [INSPIRE].
P.-J. De Smet and C.D. White, Extended solutions for the biadjoint scalar field, Phys. Lett. B 775 (2017) 163 [arXiv:1708.01103] [INSPIRE].
W.D. Goldberger and A.K. Ridgway, Bound states and the classical double copy, Phys. Rev. D 97 (2018) 085019 [arXiv:1711.09493] [INSPIRE].
M. Carrillo-González, R. Penco and M. Trodden, The classical double copy in maximally symmetric spacetimes, JHEP 04 (2018) 028 [arXiv:1711.01296] [INSPIRE].
N. Bahjat-Abbas, A. Luna and C.D. White, The Kerr-Schild double copy in curved spacetime, JHEP 12 (2017) 004 [arXiv:1710.01953] [INSPIRE].
A. Luna, I. Nicholson, D. O’Connell and C.D. White, Inelastic Black Hole Scattering from Charged Scalar Amplitudes, JH EP 03 (2018) 044 [arXiv:1711.03901] [INSPIRE].
C.-H. Shen, Gravitational Radiation from Color-Kinematics Duality, JHEP 11 (2018) 162 [arXiv:1806.07388] [INSPIRE].
A. Ilderton, Screw-symmetric gravitational waves: a double copy of the vortex, Phys. Lett. B 782 (2018) 22 [arXiv:1804.07290] [INSPIRE].
D.S. Berman, E. Chacón, A. Luna and C.D. White, The self-dual classical double copy, and the Eguchi-Hanson instanton, JHEP 01 (2019) 107 [arXiv:1809.04063] [INSPIRE].
N. Bahjat-Abbas, R. Stark-Muchão and C.D. White, Biadjoint wires, Phys. Lett. B 788 (2019) 274 [arXiv:1810.08118] [INSPIRE].
J. Plefka, J. Steinhoff and W. Wormsbecher, Effective action of dilaton gravity as the classical double copy of Yang-Mills theory, Phys. Rev. D 99 (2019) 024021 [arXiv:1807.09859] [INSPIRE].
M. Gurses and B. Tekin, Classical Double Copy: Kerr-Schild-Kundt metrics from Yang-Mills Theory, Phys. Rev. D 98 (2018) 126017 [arXiv:1810.03411] [INSPIRE].
G.L. Cardoso, S. Nagy and S. Nampuri, A double copy for \( \mathcal{N} \) = 2 supergravity: a linearised tale told on-shell, JHEP 10 (2016) 127 [arXiv:1609.05022] [INSPIRE].
G. Cardoso, S. Nagy and S. Nampuri, Multi-centered \( \mathcal{N} \) = 2 BPS black holes: a double copy description, JHEP 04 (2017) 037 [arXiv:1611.04409] [INSPIRE].
G. Lopes Cardoso, G. Inverso, S. Nagy and S. Nampuri, Comments on the double copy construction for gravitational theories, PoS CORFU2017 (2018) 177 [arXiv:1803.07670] [INSPIRE].
K. Andrzejewski and S. Prencel, From polarized gravitational waves to analytically solvable electromagnetic beams, Phys. Rev. D 100 (2019) 045006 [arXiv:1901.05255] [INSPIRE].
J. Plefka, C. Shi, J. Steinhoff and T. Wang, Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO, Phys. Rev. D 100 (2019) 086006 [arXiv:1906.05875] [INSPIRE].
M. Carrillo González, B. Melcher, K. Ratliff, S. Watson and C.D. White, The classical double copy in three spacetime dimensions, JHEP 07 (2019) 167 [arXiv:1904.11001] [INSPIRE].
S. Sabharwal and J.W. Dalhuisen, Anti-Self-Dual Spacetimes, Gravitational Instantons and Knotted Zeros of the Weyl Tensor, JHEP 07 (2019) 004 [arXiv:1904.06030] [INSPIRE].
I. Bah, R. Dempsey and P. Weck, Kerr-Schild Double Copy and Complex Worldlines, JHEP 02 (2020) 180 [arXiv:1910.04197] [INSPIRE].
L. Borsten, I. Jubb, V. Makwana and S. Nagy, Gauge × gauge on spheres, JHEP 06 (2020) 096 [arXiv:1911.12324] [INSPIRE].
L. Borsten, H. Kim, B. Jurčo, T. Macrelli, C. Sämann and M. Wolf, Double Copy from Homotopy Algebras, Fortsch. Phys. 69 (2021) 2100075 [arXiv:2102.11390] [INSPIRE].
L. Borsten, I. Jubb, V. Makwana and S. Nagy, Gauge × gauge = gravity on homogeneous spaces using tensor convolutions, JHEP 06 (2021) 117 [arXiv:2104.01135] [INSPIRE].
N. Bahjat-Abbas, R. Stark-Muchão and C.D. White, Monopoles, shockwaves and the classical double copy, JHEP 04 (2020) 102 [arXiv:2001.09918] [INSPIRE].
G. Elor, K. Farnsworth, M.L. Graesser and G. Herczeg, The Newman-Penrose Map and the Classical Double Copy, JHEP 12 (2020) 121 [arXiv:2006.08630] [INSPIRE].
T. Adamo and A. Ilderton, Classical and quantum double copy of back-reaction, JHEP 09 (2020) 200 [arXiv:2005.05807] [INSPIRE].
L. Alfonsi, C.D. White and S. Wikeley, Topology and Wilson lines: global aspects of the double copy, JHEP 07 (2020) 091 [arXiv:2004.07181] [INSPIRE].
C. Keeler, T. Manton and N. Monga, From Navier-Stokes to Maxwell via Einstein, JHEP 08 (2020) 147 [arXiv:2005.04242] [INSPIRE].
D.A. Easson, C. Keeler and T. Manton, Classical double copy of nonsingular black holes, Phys. Rev. D 102 (2020) 086015 [arXiv:2007.16186] [INSPIRE].
O. Pasarin and A.A. Tseytlin, Generalised Schwarzschild metric from double copy of point-like charge solution in Born-Infeld theory, Phys. Lett. B 807 (2020) 135594 [arXiv:2005.12396] [INSPIRE].
M.K. Gumus and G. Alkac, More on the classical double copy in three spacetime dimensions, Phys. Rev. D 102 (2020) 024074 [arXiv:2006.00552] [INSPIRE].
R. Alawadhi, D.S. Berman, C.D. White and S. Wikeley, The single copy of the gravitational holonomy, JHEP 10 (2021) 229 [arXiv:2107.01114] [INSPIRE].
K. Lee, Kerr-Schild Double Field Theory and Classical Double Copy, JHEP 10 (2018) 027 [arXiv:1807.08443] [INSPIRE].
D.S. Berman, K. Kim and K. Lee, The classical double copy for M-theory from a Kerr-Schild ansatz for exceptional field theory, JHEP 04 (2021) 071 [arXiv:2010.08255] [INSPIRE].
E. Lescano and J.A. Rodríguez, Higher-derivative heterotic Double Field Theory and classical double copy, JHEP 07 (2021) 072 [arXiv:2101.03376] [INSPIRE].
S. Angus, K. Cho and K. Lee, The classical double copy for half-maximal supergravities and T-duality, JHEP 10 (2021) 211 [arXiv:2105.12857] [INSPIRE].
C. Cheung and J. Mangan, Covariant color-kinematics duality, JHEP 11 (2021) 069 [arXiv:2108.02276] [INSPIRE].
E. Chacón, A. Luna and C.D. White, The double copy of the multipole expansion, arXiv:2108.07702 [INSPIRE].
A. Cristofoli, R. Gonzo, D.A. Kosower and D. O’Connell, Waveforms from Amplitudes, arXiv:2107.10193 [INSPIRE].
G. Alkac, M.K. Gumus and M.A. Olpak, Kerr-Schild double copy of the Coulomb solution in three dimensions, Phys. Rev. D 104 (2021) 044034 [arXiv:2105.11550] [INSPIRE].
K. Farnsworth, M.L. Graesser and G. Herczeg, Twistor Space Origins of the Newman-Penrose Map, arXiv:2104.09525 [INSPIRE].
P. Ferrero and D. Francia, On the Lagrangian formulation of the double copy to cubic order, JHEP 02 (2021) 213 [arXiv:2012.00713] [INSPIRE].
G. Alkac, M.K. Gumus and M. Tek, The Kerr-Schild Double Copy in Lifshitz Spacetime, JHEP 05 (2021) 214 [arXiv:2103.06986] [INSPIRE].
R. Gonzo and C. Shi, Geodesics From Classical Double Copy, arXiv:2109.01072 [INSPIRE].
R. Saotome and R. Akhoury, Relationship Between Gravity and Gauge Scattering in the High Energy Limit, JHEP 01 (2013) 123 [arXiv:1210.8111] [INSPIRE].
D. Neill and I.Z. Rothstein, Classical Space-Times from the S Matrix, Nucl. Phys. B 877 (2013) 177 [arXiv:1304.7263] [INSPIRE].
A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [INSPIRE].
H. Godazgar, M. Godazgar and C.N. Pope, Taub-NUT from the Dirac monopole, Phys. Lett. B 798 (2019) 134938 [arXiv:1908.05962] [INSPIRE].
R. Alawadhi, D.S. Berman, B. Spence and D. Peinador Veiga, S-duality and the double copy, JHEP 03 (2020) 059 [arXiv:1911.06797] [INSPIRE].
A. Banerjee, E.O. Colgáin, J.A. Rosabal and H. Yavartanoo, Ehlers as EM duality in the double copy, Phys. Rev. D 102 (2020) 126017 [arXiv:1912.02597] [INSPIRE].
M. Campiglia and S. Nagy, A double copy for asymptotic symmetries in the self-dual sector, JHEP 03 (2021) 262 [arXiv:2102.01680] [INSPIRE].
R. Monteiro and D. O’Connell, The Kinematic Algebra From the Self-Dual Sector, JHEP 07 (2011) 007 [arXiv:1105.2565] [INSPIRE].
E. Casali and A. Puhm, Double Copy for Celestial Amplitudes, Phys. Rev. Lett. 126 (2021) 101602 [arXiv:2007.15027] [INSPIRE].
E. Casali and A. Sharma, Celestial double copy from the worldsheet, JHEP 05 (2021) 157 [arXiv:2011.10052] [INSPIRE].
S. Pasterski and A. Puhm, Shifting spin on the celestial sphere, Phys. Rev. D 104 (2021) 086020 [arXiv:2012.15694] [INSPIRE].
Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, Charged rotating black holes in four-dimensional gauged and ungauged supergravities, Nucl. Phys. B 717 (2005) 246 [hep-th/0411045] [INSPIRE].
A. Strominger and A. Zhiboedov, Superrotations and Black Hole Pair Creation, Class. Quant. Grav. 34 (2017) 064002 [arXiv:1610.00639] [INSPIRE].
T. Adamo and U. Kol, Classical double copy at null infinity, arXiv:2109.07832 [INSPIRE].
R. Penrose and W. Rindler, Spinors and space-time. Vol. 2: Spinor and twistor methods in space-time geometry. Cambridge University Press, (1988).
E. Newman and R. Penrose, An approach to gravitational radiation by a method of spin coefficients, J. Math. Phys. 3 (1962) 566 [INSPIRE].
R.K. Sachs, Gravitational waves in general relativity: 8. Waves in asymptotically flat space-times, Proc. Roy. Soc. Lond. A 270 (1962) 103.
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 269 (1962) 21.
H. Godazgar, M. Godazgar and C.N. Pope, Subleading BMS charges and fake news near null infinity, JHEP 01 (2019) 143 [arXiv:1809.09076] [INSPIRE].
T. Damour, Analytical calculations of gravitational radiation, in 4th Marcel Grossmann Meeting on General Relativity, R. Ruffini, ed., (1986), pp. 365–392.
D. Christodoulou, The global initial value problem in general relativity, in The 9th Marcel Grossmann meeting, V.G. Gurzadyan, R.T. Jantzen and R. Ruffini, eds., (2002), pp. 44–54, [DOI].
P.T. Chrusciel, M.A.H. MacCallum and D.B. Singleton, Gravitational waves in general relativity XIV. Bondi expansions and the ‘polyhomogeneity’ of I, Phil. Trans. Roy. Soc. A 350 (1995) 113.
P.T. Chrusciel, J. Jezierski and M.A.H. MacCallum, Uniqueness of the Trautman-Bondi mass, Phys. Rev. D 58 (1998) 084001 [gr-qc/9803010] [INSPIRE].
J.A.V. Kroon, Conserved quantities for polyhomogeneous space-times, Class. Quant. Grav. 15 (1998) 2479 [gr-qc/9805094] [INSPIRE].
J.A. Valiente-Kroon, Polyhomogeneity and zero rest mass fields with applications to Newman-Penrose constants, Class. Quant. Grav. 17 (2000) 605 [gr-qc/9907097] [INSPIRE].
R.M. Wald, General Relativity. UCP, (1984) [DOI].
M. Cvetič, C.N. Pope and A. Saha, Conformal Symmetries for Extremal Black Holes with General Asymptotic Scalars in STU Supergravity, JHEP 09 (2021) 188 [arXiv:2102.02826] [INSPIRE].
M. Chiodaroli, M. Günaydin, H. Johansson and R. Roiban, Scattering amplitudes in \( \mathcal{N} \) = 2 Maxwell-Einstein and Yang-Mills/Einstein supergravity, JHEP 01 (2015) 081 [arXiv:1408.0764] [INSPIRE].
W. Cho and K. Lee, Heterotic Kerr-Schild Double Field Theory and Classical Double Copy, JHEP 07 (2019) 030 [arXiv:1904.11650] [INSPIRE].
L. Borsten, M.J. Duff, L.J. Hughes and S. Nagy, Magic Square from Yang-Mills Squared, Phys. Rev. Lett. 112 (2014) 131601 [arXiv:1301.4176] [INSPIRE].
A. Anastasiou, L. Borsten, M.J. Duff, L.J. Hughes and S. Nagy, Yang-Mills origin of gravitational symmetries, Phys. Rev. Lett. 113 (2014) 231606 [arXiv:1408.4434] [INSPIRE].
A. Anastasiou, L. Borsten, M.J. Hughes and S. Nagy, Global symmetries of Yang-Mills squared in various dimensions, JHEP 01 (2016) 148 [arXiv:1502.05359] [INSPIRE].
A. Anastasiou et al., Twin supergravities from Yang-Mills theory squared, Phys. Rev. D 96 (2017) 026013 [arXiv:1610.07192] [INSPIRE].
A. Anastasiou, L. Borsten, M.J. Duff, S. Nagy and M. Zoccali, Gravity as Gauge Theory Squared: A Ghost Story, Phys. Rev. Lett. 121 (2018) 211601 [arXiv:1807.02486] [INSPIRE].
J.B. Griffiths, P. Krtouš and J. Podolský, Interpreting the C-metric, Class. Quant. Grav. 23 (2006) 6745 [gr-qc/0609056] [INSPIRE].
T. He, P. Mitra, A.P. Porfyriadis and A. Strominger, New Symmetries of Massless QED, JHEP 10 (2014) 112 [arXiv:1407.3789] [INSPIRE].
J. Bičák, Gravitational radiation from uniformly accelerated particles in general relativity, Proc. Roy. Soc. Lond. A 302 (1968) 201.
V. Pravda and A. Pravdova, Boost-rotation symmetric spacetimes — review, Czech. J. Phys. 50 (2000) 333, [math/0003067].
P. Sládek and J.D. Finley, III, Asymptotic properties of the C-Metric, Class. Quant. Grav. 27 (2010) 205020 [arXiv:1003.1471] [INSPIRE].
A. Tomimatsu, Power law tail of gravitational waves from a uniformly accelerating black hole, Phys. Rev. D 57 (1998) 2613 [INSPIRE].
H. Farhoosh and R.L. Zimmerman, Killing horizons around a uniformly accelerating and rotating particle, Phys. Rev. D 22 (1980) 797 [INSPIRE].
A. Ashtekar and T. Dray, On the Existence of Solutions to Einstein’s Equation With Nonzero Bondi News, Commun. Math. Phys. 79 (1981) 581 [INSPIRE].
D. Bini, C. Cherubini and B. Mashhoon, Inertial effects of an accelerating black hole, AIP Conf. Proc. 751 (2005) 37 [gr-qc/0410098] [INSPIRE].
J.W. Maluf, V.C. de Andrade and J.R. Steiner, Gravitational radiation of accelerated sources, Int. J. Mod. Phys. D 16 (2007) 857 [gr-qc/0610102] [INSPIRE].
K. Hong and E. Teo, A new form of the C metric, Class. Quant. Grav. 20 (2003) 3269 [gr-qc/0305089] [INSPIRE].
H. Godazgar, M. Godazgar and C.N. Pope, Dual gravitational charges and soft theorems, JHEP 10 (2019) 123 [arXiv:1908.01164] [INSPIRE].
H. Stephani, D. Kramer, M.A.H. MacCallum, C. Hoenselaers and E. Herlt, Exact solutions of Einstein’s field equations, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, U.K. (2003), [DOI] [INSPIRE].
R. Alawadhi, D.S. Berman and B. Spence, Weyl doubling, JHEP 09 (2020) 127 [arXiv:2007.03264] [INSPIRE].
N. Moynihan, Kerr-Newman from Minimal Coupling, JHEP 01 (2020) 014 [arXiv:1909.05217] [INSPIRE].
M.-Z. Chung, Y.-T. Huang and J.-W. Kim, Kerr-Newman stress-tensor from minimal coupling, JHEP 12 (2020) 103 [arXiv:1911.12775] [INSPIRE].
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Godazgar, H., Godazgar, M., Monteiro, R. et al. Asymptotic Weyl double copy. J. High Energ. Phys. 2021, 126 (2021). https://doi.org/10.1007/JHEP11(2021)126
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DOI: https://doi.org/10.1007/JHEP11(2021)126