Classical Double Copy: Kerr-Schild-Kundt metrics from Yang-Mills Theory

Abstract

The classical double copy idea relates some solutions of Einstein's theory with those of gauge and scalar field theories. We study the Kerr-Schild-Kundt (KSK) class of metrics in $d$-dimensions in the context of possible new examples of this idea. We first show that it is possible to solve the Einstein-Yang-Mills system exactly using the solutions of a Klein-Gordon type scalar equation when the metric is the $pp$-wave metric which is the simplest member of the KSK class. In the more general KSK class, the solutions of a scalar equation also solve the Yang-Mills, Maxwell and Einstein-Yang-Mills-Maxwell equations exactly albeit with a null fluid source. Hence in the general KSK class, the double copy correspondence is not as clean-cut as in the case of the $pp$-wave. In our treatment all the gauge fields couple to dynamical gravity, and are not treated as test fields. We also briefly study Gödel type metrics along the same lines.

9 pages, published version, in v3 small typos are corrected

References in corpus (6)

• New Relations for Gauge-Theory Amplitudes
• Black holes and the double copy
• Kerr-Schild Double Field Theory and Classical Double Copy
• AdS Waves as Exact Solutions to Quadratic Gravity
• New Exact Solutions of Quadratic Curvature Gravity
• AdS-plane wave and pp-wave solutions of generic gravity theories

Cited by in corpus (34)

• Double copy for massive quantum particles with spin
• Double Copy for Celestial Amplitudes
• The classical double copy of non-singular black holes
• Ehlers as EM duality in the double copy
• Weyl doubling
• Heterotic Kerr-Schild Double Field Theory and Classical Double Copy
• UV considerations on scattering amplitudes in a web of theories
• Asymptotic Weyl Double Copy
• Loop-Level Double-Copy for Massive Quantum Particles
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• On the Lagrangian formulation of the double copy to cubic order
• Isometries and the double copy
• Geodesics From Classical Double Copy
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• The Weyl double copy in vacuum spacetimes with a cosmological constant
• Higher-derivative Heterotic Double Field Theory and Classical Double Copy
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• Weyl double copy and massless free fields in curved spacetimes
• From polarized gravitational waves to analytically solvable electromagnetic beams
• Black Hole Horizons from the Double Copy
• Extracting Einstein from the Loop-Level Double-Copy
• The Classical Double Copy for Half-Maximal Supergravities and T-duality
• The classical double copy in curved spacetimes: Perturbative Yang-Mills from the bi-adjoint scalar
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Note on the asymptotic structure of Kerr-Schild form
• Classical double copy and higher-spin fields
• Kerr-Schild double copy for Kundt spacetimes of any dimension
• Background ambiguity and the Gödel double copy
• New framework for classical double copies
• Revisiting the dynamics of a charged spinning body in curved spacetime
• Rotation in vacuum and scalar background: are there alternatives to Newman-Janis algorithm?
• All non-expanding gravitational waves in $D$-dimensional (anti-)de Sitter space
• Untwisting the double copy: the zeroth copy as an optical seed
• NS-NS Spacetimes from Amplitudes