Abstract
Gauge-gravity duality is arguably our best hope for understanding quantum gravity. Considerable progress has been made in relating scattering amplitudes in certain gravity theories to those in gauge theories — a correspondence dubbed the double copy. Recently, double copies have also been realized in a classical setting, as maps between exact solutions of gauge theories and gravity. We present here a novel map between a certain class of real, exact solutions of Einstein’s equations and self-dual solutions of the flat-space vacuum Maxwell equations. This map, which we call the Newman-Penrose map, is well-defined even for non-vacuum, non-stationary spacetimes, providing a systematic framework for exploring gravity solutions in the context of the double copy that have not been previously studied in this setting. To illustrate this, we present here the Newman- Penrose map for the Schwarzschild and Kerr black holes, and Kinnersley’s photon rocket.
Highlights
Tree level [2], appear to hold at loop level [3, 6,7,8,9,10], and are widely believed to hold to all orders in perturbation theory [11, 12]
In this work we introduce the Newman-Penrose map — a novel map, closely related to the classical double copy, that associates a self-dual solution of the vacuum Maxwell equations to certain Kerr-Schild spacetimes that need be neither stationary nor pure vacuum
The Newman-Penrose map defined in the previous subsection is, a priori, independent of the usual Kerr-Schild double copy which we reviewed in section 2.1, and one would not necessarily expect there to be any clear relationship between the real gauge fields associated with each prescription
Summary
We briefly review the Kerr-Schild classical double copy, and summarize the result for Schwarzschild spacetime. We review the zeroth and single copy relating solutions in gauge theory to bi-adjoint scalar theory. Of the self-dual double copy [20], the formalism of which parallels some of the framework introduced here
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