More on the Classical Double Copy in Three Spacetime Dimensions

Abstract

It is well-known that General Relativity (GR) in three spacetime dimensions (3D) has no well-defined Newtonian limit. Recently, a static solution mimicking the behaviour of the expected Newtonian potential has been found in arXiv:1904.11001 by studying the classical double copy of a point charge in gauge theory. This is the first example where the vacuum solution in the gauge theory leads to a non-vacuum solution on the gravity side. The resulting energy-momentum tensor was attributed to a free scalar ghost field; however, alternatively, the source can be seen as one resulting from a spacelike perfect fluid. In this paper, we first give an alternative derivation of the solution where there is no need to perform a generalized gauge transformation to obtain a quadratic Lagrangian without propagating ghost fields. Then, we present a stationary version of the solution and show that the scalar field interpretation of the source does not survive in this case, leaving the spacelike fluid as the only possibility. We give the gauge theory single copy of our solution and comment on the implications of our results on the validity of the classical double copy in 3D. The effect of the cosmological constant is also discussed.

11 pages, no figures, minor changes, version to appear in PRD

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• New heavenly double copies
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• Scattering Amplitudes and the Double Copy in Topologically Massive Theories
• The double copy of the multipole expansion
• Generalized Black Holes in 3D Kerr-Schild Double Copy
• The classical double copy in curved spacetimes: Perturbative Yang-Mills from the bi-adjoint scalar
• Regularized Weyl double copy
• Note on the asymptotic structure of Kerr-Schild form
• Weyl double copy in type D spacetime in four and five dimensions
• The Weyl double copy from twistor space
• Five dimensional Weyl double copy
• Classical double copy in the black hole mini-superspace
• The Kerr-Schild Double Copy in Lifshitz Spacetime
• NS-NS Spacetimes from Amplitudes