TY - JOUR

T1 - Ehlers transformations as em duality in the double copy

AU - Banerjee, A.

AU - O Colgain, E.

AU - Rosabal, J. A.

AU - Yavartanoo, H.

N1 - Publisher Copyright:
© 2020 authors. Published by the American Physical Society.

PY - 2020/12/11

Y1 - 2020/12/11

N2 - 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 σ model with target space geometry SU(1,1)/U(1). Thus, any transformation by SU(1,1)≅SL(2,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)⊂SL(2,R) symmetry dual to EM duality in the single copy. Moreover, we extend the analysis to Einstein-Maxwell theory, where we highlight the role of Ehlers-Harrison transformations and, for spherically symmetric charged black hole solutions, we interpret the equations of motion as a truncation of the putative single copy for Einstein-Yang-Mills theory.

AB - 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 σ model with target space geometry SU(1,1)/U(1). Thus, any transformation by SU(1,1)≅SL(2,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)⊂SL(2,R) symmetry dual to EM duality in the single copy. Moreover, we extend the analysis to Einstein-Maxwell theory, where we highlight the role of Ehlers-Harrison transformations and, for spherically symmetric charged black hole solutions, we interpret the equations of motion as a truncation of the putative single copy for Einstein-Yang-Mills theory.

UR - http://www.scopus.com/inward/record.url?scp=85097973687&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.102.126017

DO - 10.1103/PhysRevD.102.126017

M3 - Article

AN - SCOPUS:85097973687

SN - 2470-0010

VL - 102

JO - Physical Review D

JF - Physical Review D

IS - 12

M1 - 126017

ER -