K-essence Lagrangians that can source Kerr-Schild spacetimes must be at most quadratic in the kinetic term, and linear when the congruence is autoparallel or when linearized solutions are also exact.
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K-essence sources of Kerr-Schild spacetimes
K-essence Lagrangians that can source Kerr-Schild spacetimes must be at most quadratic in the kinetic term, and linear when the congruence is autoparallel or when linearized solutions are also exact.