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

Abstract

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" 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 Friedrich-Nagy gauge for systems with two commuting spacelike 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." © 2014 American Physical Society.