Abstract
Recently, a perturbative duality between gauge and gravity theories (the double copy) has been discovered, that is believed to hold to all loop orders. In this paper, we examine the relationship between classical solutions of non-Abelian gauge theory and gravity. We propose a general class of gauge theory solutions that double copy to gravity, namely those involving stationary Kerr-Schild metrics. The Schwarzschild and Kerr black holes (plus their higher-dimensional equivalents) emerge as special cases. We also discuss plane wave solutions. Furthermore, a recently examined double copy between the self-dual sectors of Yang-Mills theory and gravity can be reinterpreted using a momentum-space generalisation of the Kerr-Schild framework.
Highlights
By this, one may ask whether any features of the double copy manifest themselves in a classical context
We examine the relationship between classical solutions of non-Abelian gauge theory and gravity
We propose a general class of gauge theory solutions that double copy to gravity, namely those involving stationary Kerr-Schild metrics
Summary
We will review the well-known double copy story for amplitudes [1,2,3]. BCJ duality is the statement that, for each such Jacobi identity, the kinematic numerators (as functions of the set of independent external and loop momenta) can be chosen to obey the same relation. We take this as an indication that some kinematic symmetry algebra underlying the numerators exists. In some cases (such as the self-dual sector of Yang-Mills theory), BCJ duality can be made exact at the Lagrangian level, and the kinematic symmetry interpreted [49] We will use the Minkowski metric diag(−, +, +, +, . . .) throughout, unless otherwise stated
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