Abstract
We use the classical double copy to identify a necessary condition for Maxwell theory sources to constitute single copies of Kerr-Schild solutions to Einstein’s equations. In the case of four-dimensional Kerr-Schild spacetimes on Minkowski backgrounds, we extend this condition to a parameterization of the corresponding single copies. These are given by Líenard-Wiechert fields of charges on complex worldlines. This unifies the known instances of the Kerr-Schild double copy black holes on flat four-dimensional backgrounds into a single framework. Furthermore, we use the more generic condition identified to show why the black ring in five dimensions does not admit Kerr-Schild coordinates.
References
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, T. Dennen, Y.-t. Huang and M. Kiermaier, Gravity as the Square of Gauge Theory, Phys. Rev. D 82 (2010) 065003 [arXiv:1004.0693] [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.P. Kerr and A. Schild, Republication of: A new class of vacuum solutions of the Einstein field equations, Gen. Rel. Grav. 41 (2009) 2485.
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, I. Nicholson and D. O’Connell, Type D Spacetimes and the Weyl Double Copy, Class. Quant. Grav. 36 (2019) 065003 [arXiv:1810.08183] [INSPIRE].
A. Ilderton, Screw-symmetric gravitational waves: a double copy of the vortex, Phys. Lett. B 782 (2018) 22 [arXiv:1804.07290] [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].
M. Carrillo-González, R. Penco and M. Trodden, The classical double copy in maximally symmetric spacetimes, JHEP 04 (2018) 028 [arXiv:1711.01296] [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].
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].
Y. Choquet-Bruhat and R.P. Geroch, Global aspects of the Cauchy problem in general relativity, Commun. Math. Phys. 14 (1969) 329 [INSPIRE].
E.T. Newman, Maxwell fields and shear free null geodesic congruences, Class. Quant. Grav. 21 (2004) 3197 [gr-qc/0402056] [INSPIRE].
E. Newman and R. Penrose, An Approach to gravitational radiation by a method of spin coefficients, J. Math. Phys. 3 (1962) 566 [INSPIRE].
P. Nurowski and A. Taghavi-Chabert, A Goldberg-Sachs theorem in dimension three, Class. Quant. Grav. 32 (2015) 115009 [arXiv:1502.00304] [INSPIRE].
E.T. Newman and A.I. Janis, Note on the Kerr spinning particle metric, J. Math. Phys. 6 (1965) 915 [INSPIRE].
H. Erbin, Janis-newman algorithm: Generating rotating and nut charged black holes, Universe 3 (2017) 19.
J.B. Griffiths and J. Podolský, A New look at the Plebański-Demiański family of solutions, Int. J. Mod. Phys. D 15 (2006) 335 [gr-qc/0511091] [INSPIRE].
S. Caser, Electrodynamics in Dirac’s Gauge: A Geometrical Equivalence, Found. Phys. Lett. 14 (2001) 263.
R. Emparan and H.S. Reall, Black Holes in Higher Dimensions, Living Rev. Rel. 11 (2008) 6 [arXiv:0801.3471] [INSPIRE].
R. Emparan and H.S. Reall, Black Rings, Class. Quant. Grav. 23 (2006) R169 [hep-th/0608012] [INSPIRE].
B. Ett and D. Kastor, An Extended Kerr-Schild Ansatz, Class. Quant. Grav. 27 (2010) 185024 [arXiv:1002.4378] [INSPIRE].
T. Málek and V. Pravda, Kerr-Schild spacetimes with (A)dS background, Class. Quant. Grav. 28 (2011) 125011 [arXiv:1009.1727] [INSPIRE].
Z. Mirzaiyan, B. Mirza and E. Sharifian, Generating five-dimensional Myers-Perry black hole solution using quaternions, Annals Phys. 389 (2018) 11 [arXiv:1708.08969] [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].
R.W. Lind and E.T. Newman, Complexification of the algebraically special gravitational fields, J. Math. Phys. 15 (1974) 1103.
E.T. Newman, Lìenard-wiechert fields and general relativity, J. Math. Phys. 15 (1974) 44.
G.C. Debney, R.P. Kerr and A. Schild, Solutions of the Einstein and Einstein-Maxwell Equations, J. Math. Phys. 10 (1969) 1842 [INSPIRE].
J.N. Goldberg and R.K. Sachs, Republication of: A theorem on petrov types, Gen. Rel. Grav. 41 (2009) 433.
A.Z. Petrov, The classification of spaces defining gravitational fields, Gen. Rel. Grav. 32 (2000) 1665.
A.H. Bilge and M. Gürses, Generalized kerr-schild transformation, in Group Theoretical Methods in Physics, M. Serdaroğlu and E. Ínönü, eds., pp. 252, Springer Berlin Heidelberg, Germany, (1983).
W. Chen and H. Lü, Kerr-Schild structure and harmonic 2-forms on (A)dS-Kerr-NUT metrics, Phys. Lett. B 658 (2008) 158 [arXiv:0705.4471] [INSPIRE].
W. Israel, Source of the kerr metric, Phys. Rev. D 2 (1970) 641 [INSPIRE].
H. Balasin and H. Nachbagauer, Distributional energy momentum tensor of the Kerr-Newman space-time family, Class. Quant. Grav. 11 (1994) 1453 [gr-qc/9312028] [INSPIRE].
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ArXiv ePrint: 1910.04197
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Bah, I., Dempsey, R. & Weck, P. Kerr-Schild double copy and complex worldlines. J. High Energ. Phys. 2020, 180 (2020). https://doi.org/10.1007/JHEP02(2020)180
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DOI: https://doi.org/10.1007/JHEP02(2020)180
Keywords
- Black Holes
- Classical Theories of Gravity
- Gauge-gravity correspondence