A generalization of the Lorentz ether to gravity with general-relativistic limit

We define a class of condensed matter theories in a Newtonian framework with a Lagrange formalism so that a variant of Noether’s theorem gives the classical conservation laws: ∂tρ+ ∂i(ρv ) = 0 ∂t(ρv ) + ∂i(ρv v + p) = 0. We show that for the metric gμν defined by ĝ = g √−g = ρ ĝ = g √−g = ρv ĝ = g √−g = ρvv + p these theories are equivalent to a metric theory of gravity with Lagrangian L = LGR + Lmatter(gμν , φ )− (8πG)(Υg − Ξδijg) √−g. with covariant Lmatter , which defines a generalization of the Lorentz ether to gravity. Thus, the Einstein equivalence may be derived from simple condensed matter axioms. The Einstein equations appear in a natural limit Ξ,Υ → 0.