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

I. Schmelzer
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Abstract

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 ρ+ \partial_i (ρv^i) = 0 \partial_t (ρv^j) + \partial_i (ρv^i v^j + p^{ij}) = 0 We show that for an algebraically defined ``effective Lorentz metric'' g_{μν} and ``effective matter fields'' ϕthese theories are equivalent to material models of a metric theory of gravity with Lagrangian L = L_{GR} + L_{matter} - (8πG)^{-1}(Υg^{00}-Ξ(g^{11}+g^{22}+g^{33}))\sqrt{-g} which fulfils the Einstein equivalence principle and leads to the Einstein equations in the limit Ξ,Υ\to 0.

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I. Schmelzer. 2001-04-04. Derivation of the Einstein Equivalence Principle in a Class of Condensed Matter Theories. https://arxiv.org/abs/gr-qc/0104013

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