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.
Minimally coupled scalar fields as imperfect fluids
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abstract
We revisit the issue of the fluid description of minimally coupled scalar fields. While in a cosmological setup the interpretation of a time-evolving scalar field as a perfect fluid is well-understood, the situation is more intricate when the scalar field is static, but has a spatial gradient, a situation motivated by black hole perturbations in scalar-tensor theories. Then the scalar field is interpreted as either a particular imperfect fluid of type I or a superposition of a pair of leftgoing (incoming) and rightgoing (outgoing) null dusts with a perfect fluid. Finally, when the scalar gradient is null, it is equivalent to an imperfect fluid of type II, degenerating into null dust when the energy conditions are imposed. We also propose the suitable action in terms of the fluid pressure components for each case and discuss the variational principle for a generic class of minimally coupled scalar fields.
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gr-qc 1years
2025 1verdicts
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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.