Kerr-Schild Double Field Theory and Classical Double Copy

TL;DR

This paper extends the Kerr-Schild formalism to double field theory and supergravity, enabling the construction of solutions and a classical double copy structure within the massless string NS-NS sector, including supersymmetric cases.

Contribution

It introduces a generalized Kerr-Schild ansatz for DFT, constructs related field and Killing spinor equations, and extends the classical double copy to supergravity and supersymmetric solutions.

Findings

Generalized Kerr-Schild ansatz for DFT is formulated.

Solutions can be found via linear equations despite quadratic field equations.

Classical double copy structure is extended to the NS-NS sector and supersymmetric solutions.

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.