Kerr-Schild Double Copy of the Coulomb Solution in Three Dimensions

Abstract

While the Kerr-Schild double copy of the Coulomb solution in dimensions higher than three is the Schwarzschild black hole, it is known that it should be a non-vacuum solution in three dimensions. We show that the static black hole solution of Einstein-Maxwell theory (with one ghost sign in the action) is the double copy with the correct Newtonian limit, which provides an improvement over the previous construction with a free scalar field that does not vanish at infinity. By considering a negative cosmological constant, we also study the charged Bañados-Teitelboim-Zanelli black hole and find that the single copy gauge field is the Coulomb solution modified by a term which describes an electric field linearly increasing with the radial coordinate, which is the usual behaviour of the Schwarzschild-AdS black hole in higher dimensions when written around a flat background metric.

15 pages + references, typos in equations (3.1) and (3.3) corrected, minor changes, version to appear in PRD (with three additional references)

References in corpus (14)

• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Black holes and the double copy
• The Kerr-Schild double copy in curved spacetime
• Yang-Mills origin of gravitational symmetries
• A Twistorial Foundation for the Classical Double Copy
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• The Classical Double Copy of a Point Charge
• Regular black holes in three dimensions
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• Twistor Space Origins of the Newman-Penrose Map
• More on the Classical Double Copy in Three Spacetime Dimensions
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Cited by in corpus (22)

• Asymptotic Weyl Double Copy
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• Alternative formulations of the twistor double copy
• The double copy of the multipole expansion
• Why is the Weyl double copy local in position space?
• Non-perturbative aspects of the self-dual double copy
• Isometries and the double copy
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• Generalized Black Holes in 3D Kerr-Schild Double Copy
• Black Hole Horizons from the Double Copy
• The Classical Double Copy for Half-Maximal Supergravities and T-duality
• Regularized Weyl double copy
• A spinorial double copy for $\mathcal{N}=0$ supergravity
• Note on the asymptotic structure of Kerr-Schild form
• Electromagnetic Generalized Quasi-topological gravities in $(2+1)$ dimensions
• On regular charged black holes in three dimensions
• Weyl double copy in type D spacetime in four and five dimensions
• Five dimensional Weyl double copy
• New framework for classical double copies
• Classical double copy in the black hole mini-superspace
• Massive Covariant Colour-Kinematics in 3D
• NS-NS Spacetimes from Amplitudes