Kerr-Schild Double Field Theory and Classical Double Copy

Abstract

The Kerr-Schild (KS) formalism is a powerful tool for constructing exact solutions in general relativity. In this paper, we present a generalization of the conventional KS formalism to double field theory (DFT) and supergravities. We introduce a generalized KS ansatz for the generalized metric in terms of a pair of null vectors. Applying this ansatz to the equations of motion of DFT, we construct the generalized KS field equation. While the generalized KS equations are quadratic in the fields, we show that it is possible to find solutions by considering linear equations only. Furthermore, we construct a Killing spinor equation under the generalized KS ansatz. Based on this formalism, we show that the classical double copy structure, which represents solutions of the Einstein equation in terms of solutions of the Maxwell equation, can be extended to the entire massless string NS-NS sector. We propose a supersymmetric classical double copy which shows that solutions of the Killing spinor equation can be realized in terms of solutions of the BPS equation of the supersymmetric Maxwell theory.

40 pages

References in corpus (17)

• Double Field Theory
• Black holes and the double copy
• The gauge algebra of double field theory and Courant brackets
• Generalized Geometry and M theory
• The Kinematic Algebra From the Self-Dual Sector
• Differential geometry with a projection: Application to double field theory
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Gauged Double Field Theory
• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• Double Field Theory Formulation of Heterotic Strings
• Yang-Mills origin of gravitational symmetries
• Heterotic $\alpha$'-corrections in Double Field Theory
• A double copy for $\mathcal{N}=2$ supergravity: a linearised tale told on-shell
• Screw-symmetric gravitational waves: a double copy of the vortex
• KLT relations from the Einstein-Hilbert Lagrangian
• Twofold Symmetries of the Pure Gravity Action
• Einstein Double Field Equations

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