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