Generalized unimodular gravity is shown to admit a Henneaux-Teitelboim-like action; for constant barotropic index the action is local, and for W=-1 it reduces to the unimodular gravity action.
Do gravitational fields play an essential part in the structure of the elementary particles of matter?,
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Alternative Action for Generalized Unimodular Gravity
Generalized unimodular gravity is shown to admit a Henneaux-Teitelboim-like action; for constant barotropic index the action is local, and for W=-1 it reduces to the unimodular gravity action.