A non-variational method for coupling scalar fields to gravity reproduces known models and produces asymptotically Kasner Bianchi I solutions under specific conditions.
and Mathews, G.J.Relativistic numerical hydrodynamics, volume 232
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A general formalism for coupling scalar fields to the Einstein equations without a variational principle
A non-variational method for coupling scalar fields to gravity reproduces known models and produces asymptotically Kasner Bianchi I solutions under specific conditions.