Background ambiguity and the Gödel double copy

Abstract

In this work, we investigate the assumptions regarding spacetime backgrounds underlying the classical double copy. We argue (contrary to the norm) that single-copy fields naturally constructed on the original curved background metric are only interpretable on a flat metric when such a well-defined limit exists, for which Kerr--Schild coordinates offer a natural choice. As an explicit example where such a distinction matters, we initiate an exploration of single-copies for the Gödel universe. This metric lacks a (geodesic) Kerr--Schild representation yet is Petrov type-D, meaning the technology of the ``Weyl double copy" may be utilized. The Weyl derived single copy has many desirable features, including matching the defining properties of the spacetime, and being sourced by the mixed Ricci tensor just as Kerr--Schild single copies are. To compare, we propose a sourced flat-space single-copy interpretation for the Gödel metric by leveraging its symmetries, and find that this proposal lacks the defining properties of the spacetime, and is not consistent with the flat limit of our curved-space single copy. Notably, this inconsistency does not occur in Kerr--Schild metrics. Our curved-space single copy also lead to the same electromagnetic analogue of the Gödel universe found separately through tidal force analogies, opening a new avenue of exploration between the double copy and gravitoelectromagnetism programs.

arXiv comment29 pages, 2 figures. Updated to reflect changes made for version published in JHEP

References in corpus (27)

• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Black holes and the double copy
• A new look at the Plebanski-Demianski family of solutions
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Type D Spacetimes and the Weyl Double Copy
• A gravito-electromagnetic analogy based on tidal tensors
• The Weyl Double Copy for Gravitational Waves
• Screw-symmetric gravitational waves: a double copy of the vortex
• Gravito-electromagnetic analogies
• The classical double copy of non-singular black holes
• The Newman-Penrose Map and the Classical Double Copy
• Classical Double Copy: Kerr-Schild-Kundt metrics from Yang-Mills Theory
• Einstein-Maxwell theory and the Weyl double copy
• Alternative formulations of the twistor double copy
• Godel-Type Metrics in Various Dimensions
• Twistor Space Origins of the Newman-Penrose Map
• Sagnac Effect of Goedel's Universe
• Why is the Weyl double copy local in position space?
• Isometries and the double copy
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• From polarized gravitational waves to analytically solvable electromagnetic beams
• Black Hole Horizons from the Double Copy
• Godel-type Metrics in Various Dimensions II: Inclusion of a Dilaton Field
• Regularized Weyl double copy
• A spinorial double copy for $\mathcal{N}=0$ supergravity
• Kerr-Schild double copy for Kundt spacetimes of any dimension

Cited by in corpus (2)

• Gravito-electromagnetism, Kerr-Schild and Weyl double copies; a unified perspective
• New framework for classical double copies