Derivation of the Einstein Equivalence Principle in a Class of Condensed Matter Theories
Abstract
Description
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.
22 pages Latex, no figures. More detailed version of parts of gr-qc/0001101
22 pages Latex, no figures. More detailed version of parts of gr-qc/0001101