Numerical solutions to Einstein's equations in a shearing-dust Universe: a code comparison

Abstract

A number of codes for general-relativistic simulations of cosmological structure formation have been developed in recent years. Here we demonstrate that a sample of these codes produce consistent results beyond the Newtonian regime. We simulate solutions to Einstein's equations dominated by gravitomagnetism -- a vector-type gravitational field that doesn't exist in Newtonian gravity and produces frame-dragging, the leading-order post-Newtonian effect. We calculate the coordinate-invariant effect on intersecting null geodesics by performing ray tracing in each independent code. With this observable quantity, we assess and compare each code's ability to compute relativistic effects.

14 pages, 5 figures, accepted to CQG