Galilean first-order formulation for the nonrelativistic expansion of general relativity
Dennis Schrøder Hansen, Jelle Hartong, Niels A. Obers, Gerben Oling
Abstract
We reformulate the Palatini action for general relativity in terms of moving frames that exhibit local Galilean covariance in a large speed of light expansion. For this, we express the action in terms of variables that are adapted to a Galilean subgroup of the $\mathrm{GL}(n,\mathbb{R})$ structure group of a general frame bundle. This leads to a novel Palatini-type formulation of general relativity that provides a natural starting point for a first-order nonrelativistic expansion. In doing so, we show how a comparison of Lorentzian and Newton-Cartan metric compatibility explains the appearance of torsion in the nonrelativistic expansion.
Topics & Concepts
GalileanGeneral relativityMathematical physicsPhysicsGalilean invarianceTheory of relativityClassical mechanicsMathematicsTheoretical physicsBlack Holes and Theoretical PhysicsCosmology and Gravitation TheoriesAdvanced Differential Geometry Research