The Weyl double copy in vacuum spacetimes with a cosmological constant

Abstract

We examine the Weyl double copy relation for vacuum solutions of the Einstein equations with a cosmological constant using the approach we previously described, in which the spin-1/2 massless free-field spinors (Dirac-Weyl fields) are regarded as basic units. Based on the exact non-twisting vacuum type N and vacuum type D solutions, the finding explicitly shows that the single and zeroth copies fulfill conformally invariant field equations in conformally flat spacetime. In addition, irrespective of the presence of a cosmological constant, we demonstrate that the zeroth copy connects Dirac-Weyl fields with the degenerate electromagnetic fields in the curved spacetime in addition to connecting gravity fields with the single copy in conformally flat spacetime. Moreover, the study also demonstrates the critical significance the zeroth copy plays in time-dependent radiation solutions. In particular, for Robinson-Trautman (Λ) gravitational waves, unlike the single copy, we find that the zeroth copy carries additional information to specify whether the sources of associated gravitational waves are time-like, null, or space-like, at least in the weak field limit.

Einstein-Maxwell theory and the Weyl double copy

“…Alternately, imposing the (sourced) Weyl double copy in double-field theory could be provide a mechanism to study the relation between T duality and double copy for type-D solutions. 16 Further, it would be interesting to extend our current analysis to other types of black hole spacetimes, particularly those including a cosmological constant (whose Weyl double copy was presented in [57]), additional Abelian gauge fields [58], and massless or higher-spin fields [59,60]. It would also be interesting to adapt our formalism to threedimensional spacetimes, such as the Bañados-Teitelboim-Zanelli (BTZ) black hole [61], its quantum and de Sitter generalizations [62,63], or generalized three-dimensional solutions described in [64,65].…”

Einstein-Maxwell theory and the Weyl double copy

“…Further, it would be interesting to extend our current analysis to other types of black hole spacetimes, particularly those including a cosmological constant (whose Weyl double copy was presented in [54]), additional Abelian gauge fields [55], and massless or higher spin fields [56,57].…”

Aligned fields double copy to Kerr-NUT-(A)dS

“…In this section we compute the Weyl spinor for these spacetimes and show that it can be written as the double copy of a Maxwell field. If we interpret the field as living on the curved spacetime instead of on the flat background (as is otherwise usual for single copies, see [9][10][11][50][51][52][53] for examples where the field lives on a curved background), it turns out to belong to a previously known class of Maxwell fields on Kerr-NUT-(A)dS which are aligned along the principal tensor of the spacetime [38].…”