Numerical evolution of plane gravitational waves in the Friedrich-Nagy gauge

The first proof of well-posedness of an initial boundary value problem for the Einstein equations was given in 1999 by Friedrich and Nagy. They used a frame formalism with a particular gauge for formulating the equations. This Friedrich-Nagy' (FN) gauge has never been implemented for use in numerical simulations before because it was deemed too complicated. In this paper we present an implementation of the FN gauge for systems with two commuting space-like Killing vectors. We investigate the numerical performance of this formulation for plane wave space-times, reproducing the well-known Khan-Penrose solution for colliding impulsive plane waves and exhibiting a gravitational wave ping-pong’.