A Metric Theory of Gravity with Condensed Matter Interpretation

Abstract

We consider a classical condensed matter theory in a Newtonian framework where conservation laws \partial_t ρ+ \partial_i (ρv^i) = 0 \partial_t (ρv^j) + \partial_i(ρv^i v^j + p^{ij}) = 0 are related with the Lagrange formalism in a natural way. For an ``effective Lorentz metric'' g_{μν} it is equivalent to a metric theory of gravity close to general relativity with Lagrangian L = L_{GR} - (8πG)^{-1}(Υg^{00}-Ξ(g^{11}+g^{22}+g^{33}))\sqrt{-g} We consider the differences between this theory and general relativity (no nontrivial topologies, stable frozen stars instead of black holes, big bounce instead of big bang singularity, a dark matter term), quantum gravity, and the connection with realism and Bohmian mechanics.