Derivation of the Einstein Equivalence Principle for a Class of Condensed Matter Theories

We consider 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. Thus, we have derived the Einstein equivalence from condensed matter axioms. The Einstein equations appear in the natural limit Ξ,Υ → 0.