Abstract
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
Highlights
The existence of the double copy hints at a profound relationship between gauge and gravity theories, that should transcend perturbative amplitudes
A large family of gravitational solutions was found that could be meaningfully associated with a gauge theory solution, such that the relationship between them was consistent with the BCJ double copy
√ can be chosen to define the graviton field, and κ = 32πG is the gravitational coupling constant.2. This result is obtained from eq (2.1) by replacing the gauge theory coupling constant with its gravitational counterpart, and colour factors with a second set of kinematic numerators ni
Summary
Our aim is to recall salient details about the BCJ double copy [1,2,3], that will be needed in what follows. √ can be chosen to define the graviton field, and κ = 32πG is the gravitational coupling constant.2 This result is obtained from eq (2.1) by replacing the gauge theory coupling constant with its gravitational counterpart, and colour factors with a second set of kinematic numerators ni. The gravity theory associated with the scattering amplitudes (2.3) depends on the two gauge theories from which the numerators {ni}, {ni} are taken In this paper, both will be taken from pure Yang-Mills theory, which is mapped by the double copy to “N = 0 supergravity”. Both will be taken from pure Yang-Mills theory, which is mapped by the double copy to “N = 0 supergravity” This theory is defined as Einstein gravity coupled to a scalar field φ (known as the dilaton) and a two-form Bμν (known as the Kalb-Ramond field, which can be replaced by an axion in four spacetime dimensions).
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