A polytopal discrete de Rham scheme for the exterior calculus Einstein's equations

Abstract: In this work, based on the $3+1$ decomposition in [23, 32], we present a fully exterior calculus breakdown of spacetime and Einstein's equations. Links to the orthonormal frame approach [37] are drawn to help understand the variables in this context. Two formulations are derived, discretised and tested using the exterior calculus discrete de Rham complex [12], and some discrete quantities are shown to be conserved in one of the cases.