A Metric Theory of Gravity with Condensed Matter Interpretation

Abstract

We present a metric theory of gravity with Lagrangian L = (8\pi G)^{-1}(\Xi g^{ii} - \Upsilon g^{00})\sqrt{-g} + L_{GR} + L_{matter} motivated by classical equations \partial_t \rho + \partial_i (\rho v^i) = 0 \partial_t (\rho v^j) + \partial_i (\rho v^i v^j + p^{ij}) = 0 for a medium in Newtonian space-time. We obtain stable ``frozen stars'' instead of black holes and a ``big bounce'' instead of a big bang singularity.