Abstract
The classical double copy procedure relates classical asymptotically-flat gravitational field solutions to Yang-Mills and scalar field solutions living in Minkowski space. In this paper we extend this correspondence to maximally symmetric curved spacetimes. We consider asymptotically (A)dS spacetimes in Kerr-Schild form and construct the corresponding single and zeroth copies. In order to clarify the interpretation of these copies, we study several examples including (A)dS-Schwarzschild, (A)dS-Kerr, black strings, black branes, and waves, paying particular attention to the source terms. We find that the single and zeroth copies of stationary solutions satisfy different equations than those of wave solutions. We also consider how to obtain Einstein-Maxwell solutions using this procedure. Finally, we derive the classical single and zeroth copy of the BTZ black hole.
Highlights
The BCJ relation holds both with and without supersymmetry, and even in the presence of spontaneous symmetry breaking [5]
A similar construction is possible for a de Sitter black string starting from a dSd space foliated by dSd−1, in which case the base metric reads gμν dxμdxν = sin2(z/ d) ds2dS,d−1 + dz2
In the following analysis we will use a flat base metric. This approach is different from the one we have adopted in the rest of the paper, since in the previous examples we worked with a curved base metric
Summary
We start with a concise review of the Gravity=(Yang-Mills) correspondence. The double copy procedure consists of exchanging the color factors Ci in the numerator on the r.h.s. of eq (2.1) for a second instance of kinematic factors Ni, which in general may. Be taken from a different Yang-Mills theory and differ from the Ni’s This replacement gives rise to a gravitational scattering amplitude, AG =. It is worth mentioning that, besides the double copy procedure, other relations between scattering amplitudes have been shown to exist — see for instance [6]. One such relation corresponds to the multiple trace operation of [6], which relates a gravity amplitude to an Einstein-Maxwell one. A similar relation exists between pure Yang-Mills and Yang-Mills-scalar amplitudes, where the Yang-Mills and scalar field are coupled with the usual gauge interactions [6]
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