Weyl doubling

Abstract

We study a host of spacetimes where the Weyl curvature may be expressed algebraically in terms of an Abelian field strength. These include Type D spacetimes in four and higher dimensions which obey a simple quadratic relation between the field strength and the Weyl tensor, following the Weyl spinor double copy relation. However, we diverge from the usual double copy paradigm by taking the gauge fields to be in the curved spacetime as opposed to an auxiliary flat space. We show how for Gibbons-Hawking spacetimes with more than two centres a generalisation of the Weyl doubling formula is needed by including a derivative-dependent expression which is linear in the Abelian field strength. We also find a type of twisted doubling formula in a case of a manifold with Spin(7) holonomy in eight dimensions. For Einstein Maxwell theories where there is an independent gauge field defined on spacetime, we investigate how the gauge fields determine the Weyl spacetime curvature via a doubling formula. We first show that this occurs for the Reissner-Nordström metric in any dimension, and that this generalises to the electrically-charged Born-Infeld solutions. Finally, we consider brane systems in supergravity, showing that a similar doubling formula applies. This Weyl formula is based on the field strength of the p-form potential that minimally couples to the brane and the brane world volume Killing vectors.

A double copy for asymptotic symmetries in the self-dual sector

“…The idea of gravity as a double copy (DC) 1 has found applications in the study of numerous aspects of the gravitational theory, most notably scattering amplitudes, where much of the recent success has been driven by the identification of a duality between the color and kinematic factors, the so-called Bern-Carrasco-Johannson (BCJ) duality [4][5][6][7][8][9][10][11]. It has progressed to the study of solutions, both perturbative [12][13][14][15][16][17][18] and exact [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Another important extension has been to find manifestations of it beyond gravity theory [36][37][38][39][40][41][42].…”

The Weyl double copy from twistor space

“…Since its inception, the Weyl double copy has been used to study certain topologically non-trivial electromagnetic solutions ("Hopfions") [133], and a tensorial formulation of the relationship between the electromagnetic field strength and Weyl tensor has been presented in refs. [71,73], allowing a generalisation to higher dimensions. An alternative approach to the self-dual double copy which also has links to spinorial ideas may be found in ref.…”

The single copy of the gravitational holonomy

“…ref. [76] for a related discussion), but seeking Yang-Mills solutions with a suitable SCH group might be a good place to start.…”