We consider a class of condensed matter theories in a Newtonian framework with a Lagrange formalism related in a natural way with the classical conservation laws \partial_t \rho + \partial_i (\rho v^i) = 0 \partial_t (\rho v^j) + \partial_i (\rho v^i v^j + p^{ ij}) = 0 We show that for an algebraically defined ``effective Lorentz metric'' g_{ \mu\nu} and ``effective matter fields'' \phi these theories are equivalent to material models of a metric theory of gravity with Lagrangian L = L_{ GR} + L_{ matter} - (8\pi G)^{ -1}(\Upsilon g^{ 00}-\Xi (g^{ 11}+g^{ 22}+g^{ 33}))\sqrt{ -g} which fulfils the Einstein equivalence principle and leads to the Einstein equations in the limit \Xi,\Upsilon\to 0.
Categories: gr-qc