The Newman-Penrose map and the classical double copy. (English) Zbl 1457.83031
Summary: 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.
MSC:
| 83C57 | Black holes |
| 83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 83C45 | Quantization of the gravitational field |
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