Built on

S. Sabharwal and J. W. Dalhuisen, “Anti-Self-Dual Spacetimes, Gravitational Instantons and Knotted Zeros of the Weyl Tensor,” JHEP
1904
Earlier work this paper cites.
W. Cho and K. Lee, “Heterotic Kerr-Schild Double Field Theory and Classical Double Copy,” JHEP 1907
Original
1904
Earlier work this paper cites.
I. Bakhmatov, N. S. Deger, E. T. Musaev, E. Ó Colgáin and M. M. Sheikh-Jabbari, “Tri-vector deformations in d = 11 d=11 supergravity,” JHEP 1908
Original
1906
Earlier work this paper cites.
Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson and R. Roiban, arXiv:1909.01358 [hep-th]
Original
1909
Earlier work this paper cites.
N. Moynihan, “Kerr-Newman from Minimal Coupling,” JHEP 2001
Original
1909
Earlier work this paper cites.
Y. T. Huang, U. Kol and D. O’Connell, “The Double Copy of Electric-Magnetic Duality,” arXiv:1911.06318 [hep-th]
Original
1911
Earlier work this paper cites.
R. Alawadhi, D. S. Berman, B. Spence and D. P. Veiga, “S-duality and the Double Copy,” arXiv:1911.06797 [hep-th]
Original
1911
Earlier work this paper cites.
W. D. Goldberger and J. Li, “Strings, extended objects, and the classical double copy,” arXiv:1912.01650 [hep-th]
Original
1912
Earlier work this paper cites.
K. Kim, K. Lee, R. Monteiro, I. Nicholson and D. Peinador Veiga, “The Classical Double Copy of a Point Charge,” arXiv:1912.02177 [hep-th]
Original
1912
Earlier work this paper cites.
H. A. Buchdahl, “Reciprocal Static Metrics and Scalar Fields in the General Theory of Relativity,” Phys. Rev. 115
1959
Earlier work this paper cites.
H. A. Buchdahl, “Reciprocal Static Metrics and Scalar Fields in the General Theory of Relativity,” Phys. Rev. 115
1959
Earlier work this paper cites.
J. Ehlers, “Transformations of static exterior solutions of Einstein’s gravitational field equations into different solutions by means of conformal mapping,” Colloq. Int. CNRS 91
1962
Earlier work this paper cites.
B. K. Harrison, “New Solutions of Einstein-Maxwell Equations from Old,” J. Math. Phys. 9, 1744 (1968)
1968
Earlier work this paper cites.
R. P. Geroch, “A Method for generating solutions of Einstein’s equations,” J. Math. Phys. 12
1971
Earlier work this paper cites.
P. C. Vaidya and P. V. Bhatt, “A generalized Kerr-Schild metric,” Pramana 3
1974
Earlier work this paper cites.
J. F. Plebañski, “A class of solutions of Einstein-Maxwell equations,” Annals Phys. 90
1975
Earlier work this paper cites.
J. Plebanski and M. Demianski, “Rotating, charged, and uniformly accelerating mass in general relativity,” Annals Phys. 98
1976
Earlier work this paper cites.
W. Kinnersley, “Symmetries of the Stationary Einstein-Maxwell Field Equations. 1.,” J. Math. Phys. 18
1977
Earlier work this paper cites.

Similar

W. Kinnersley and D. M. Chitre, “Symmetries of the Stationary Einstein-Maxwell Field Equations. 2.,” J. Math. Phys. 18
1977
Cited alongside, same era.
D. Maison, “Ehlers-harrison Type Transformations For Jordan’s Extended Theory Of Gravitation,” Gen. Rel. Grav. 10
1979
Cited alongside, same era.
P. Breitenlohner, D. Maison and G. W. Gibbons, “Four-Dimensional Black Holes from Kaluza-Klein Theories,” Commun. Math. Phys. 120
1988
Cited alongside, same era.
D. V. Galtsov, A. A. Garcia and O. V. Kechkin, “Symmetries of the stationary Einstein-Maxwell dilaton theory,” Class. Quant. Grav. 12
1995
Cited alongside, same era.
N. Alonso-Alberca, P. Meessen and T. Ortin, “Supersymmetry of topological Kerr-Newman-Taub-NUT-AdS space-times,” Class. Quant. Grav. 17
2000
Cited alongside, same era.

Then

L. Borsten and M. J. Duff, “Gravity as the square of Yang-Mills?,” Phys. Scripta
2015
Later among the works it cites.
A. Luna, R. Monteiro, D. O’Connell and C. D. White, “The classical double copy for Taub-NUT spacetime,” Phys. Lett. B 750
Original
2015
Later among the works it cites.
M. Chiodaroli, M. Günaydin, H. Johansson and R. Roiban, “Scattering amplitudes in 𝒩 = 2 \mathcal{N}=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity,” JHEP 1501
Original
2015
Later among the works it cites.
A. C. Petkou, P. M. Petropoulos and K. Siampos, “Geroch group for Einstein spaces and holographic integrability,” PoS PLANCK 2015
Original
2015
Later among the works it cites.
A. K. Ridgway and M. B. Wise, “Static Spherically Symmetric Kerr-Schild Metrics and Implications for the Classical Double Copy,” Phys. Rev. D 94

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2019

Ehlers as EM duality in the double copy

Banerjee, A., Colgáin, E. Ó, Rosabal, J. A. et al.

Understand

Given a solution to 4D Einstein gravity with an isometry direction, it is known that the equations of motion are identical to those of a 3D $\sigma$-model with target space geometry $SU(1,1)/U(1)$.

Thus, any transformation by $SU(1, 1) \cong SL(2,\mathbb{R})$ is a symmetry for the action and allows one to generate new solutions in 4D.
Here we clarify and extend recent work on electromagnetic (EM) duality in the context of the classical double copy.
In particular, for pure gravity, we identify an explicit map between the Maxwell field of the single copy and the scalars in the target space, allowing us to identify the $U(1) \subset SL(2, \mathbb{R})$ symmetry dual to EM duality in the single copy.

Built on

S. Sabharwal and J. W. Dalhuisen, “Anti-Self-Dual Spacetimes, Gravitational Instantons and Knotted Zeros of the Weyl Tensor,” JHEP
1904
Earlier work this paper cites.
W. Cho and K. Lee, “Heterotic Kerr-Schild Double Field Theory and Classical Double Copy,” JHEP 1907
Original
1904
Earlier work this paper cites.
I. Bakhmatov, N. S. Deger, E. T. Musaev, E. Ó Colgáin and M. M. Sheikh-Jabbari, “Tri-vector deformations in d = 11 d=11 supergravity,” JHEP 1908
Original
1906
Earlier work this paper cites.
Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson and R. Roiban, arXiv:1909.01358 [hep-th]
Original
1909
Earlier work this paper cites.
N. Moynihan, “Kerr-Newman from Minimal Coupling,” JHEP 2001
Original
1909
Earlier work this paper cites.
Y. T. Huang, U. Kol and D. O’Connell, “The Double Copy of Electric-Magnetic Duality,” arXiv:1911.06318 [hep-th]
Original
1911
Earlier work this paper cites.
R. Alawadhi, D. S. Berman, B. Spence and D. P. Veiga, “S-duality and the Double Copy,” arXiv:1911.06797 [hep-th]
Original
1911
Earlier work this paper cites.
W. D. Goldberger and J. Li, “Strings, extended objects, and the classical double copy,” arXiv:1912.01650 [hep-th]
Original
1912
Earlier work this paper cites.
K. Kim, K. Lee, R. Monteiro, I. Nicholson and D. Peinador Veiga, “The Classical Double Copy of a Point Charge,” arXiv:1912.02177 [hep-th]
Original
1912
Earlier work this paper cites.
H. A. Buchdahl, “Reciprocal Static Metrics and Scalar Fields in the General Theory of Relativity,” Phys. Rev. 115
1959
Earlier work this paper cites.
H. A. Buchdahl, “Reciprocal Static Metrics and Scalar Fields in the General Theory of Relativity,” Phys. Rev. 115
1959
Earlier work this paper cites.
J. Ehlers, “Transformations of static exterior solutions of Einstein’s gravitational field equations into different solutions by means of conformal mapping,” Colloq. Int. CNRS 91
1962
Earlier work this paper cites.
B. K. Harrison, “New Solutions of Einstein-Maxwell Equations from Old,” J. Math. Phys. 9, 1744 (1968)
1968
Earlier work this paper cites.
R. P. Geroch, “A Method for generating solutions of Einstein’s equations,” J. Math. Phys. 12
1971
Earlier work this paper cites.
P. C. Vaidya and P. V. Bhatt, “A generalized Kerr-Schild metric,” Pramana 3
1974
Earlier work this paper cites.
J. F. Plebañski, “A class of solutions of Einstein-Maxwell equations,” Annals Phys. 90
1975
Earlier work this paper cites.
J. Plebanski and M. Demianski, “Rotating, charged, and uniformly accelerating mass in general relativity,” Annals Phys. 98
1976
Earlier work this paper cites.
W. Kinnersley, “Symmetries of the Stationary Einstein-Maxwell Field Equations. 1.,” J. Math. Phys. 18
1977
Earlier work this paper cites.

Similar

W. Kinnersley and D. M. Chitre, “Symmetries of the Stationary Einstein-Maxwell Field Equations. 2.,” J. Math. Phys. 18
1977
Cited alongside, same era.
D. Maison, “Ehlers-harrison Type Transformations For Jordan’s Extended Theory Of Gravitation,” Gen. Rel. Grav. 10
1979
Cited alongside, same era.
P. Breitenlohner, D. Maison and G. W. Gibbons, “Four-Dimensional Black Holes from Kaluza-Klein Theories,” Commun. Math. Phys. 120
1988
Cited alongside, same era.
D. V. Galtsov, A. A. Garcia and O. V. Kechkin, “Symmetries of the stationary Einstein-Maxwell dilaton theory,” Class. Quant. Grav. 12
1995
Cited alongside, same era.
N. Alonso-Alberca, P. Meessen and T. Ortin, “Supersymmetry of topological Kerr-Newman-Taub-NUT-AdS space-times,” Class. Quant. Grav. 17
2000
Cited alongside, same era.

Then

L. Borsten and M. J. Duff, “Gravity as the square of Yang-Mills?,” Phys. Scripta
2015
Later among the works it cites.
A. Luna, R. Monteiro, D. O’Connell and C. D. White, “The classical double copy for Taub-NUT spacetime,” Phys. Lett. B 750
Original
2015
Later among the works it cites.
M. Chiodaroli, M. Günaydin, H. Johansson and R. Roiban, “Scattering amplitudes in 𝒩 = 2 \mathcal{N}=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity,” JHEP 1501
Original
2015
Later among the works it cites.
A. C. Petkou, P. M. Petropoulos and K. Siampos, “Geroch group for Einstein spaces and holographic integrability,” PoS PLANCK 2015
Original
2015
Later among the works it cites.
A. K. Ridgway and M. B. Wise, “Static Spherically Symmetric Kerr-Schild Metrics and Implications for the Classical Double Copy,” Phys. Rev. D 94

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

O. Lunin and J. M. Maldacena, “Deforming field theories with U(1) x U(1) global symmetry and their gravity duals,” JHEP 0505

2005

Cited alongside, same era.

D. Momeni, M. Nouri-Zonoz and R. Ramezani-Arani, “MM-NUT disk space via Ehlers transformation,” Phys. Rev. D 72

2005

Cited alongside, same era.

Z. W. Chong, G. W. Gibbons, H. Lu and C. N. Pope, “Separability and killing tensors in Kerr-Taub-NUT-de sitter metrics in higher dimensions,” Phys. Lett. B 609

2005

Cited alongside, same era.

R. B. Mann and C. Stelea, “New Taub-NUT-Reissner-Nordstrom spaces in higher dimensions,” Phys. Lett. B 632

2006

Cited alongside, same era.

Z. Bern, J. J. M. Carrasco and H. Johansson, “New Relations for Gauge-Theory Amplitudes,” Phys. Rev. D 78

Original

2008

Cited alongside, same era.

D. V. Galtsov, “Generating solutions via sigma-models,” Prog. Theor. Phys. Suppl. 172

Original

2008

Cited alongside, same era.

G. Bossard, H. Nicolai and K. S. Stelle, JHEP 07

Original

2009

Cited alongside, same era.

Original

2016