From here to infinity on a single computer

When solving Einstein's equations numerically, one faces the problem of treating an infinite asymptotically flat spacetime with finite computing resources. Here a decomposition of spacetime into hyperboloidal surfaces approaching lightlike infinity is considered. Upon compactification the Einstein equations develop formally singular terms, which can nevertheless be evaluated explicitly. Based on this method, stable numerical evolutions of spacetimes containing black holes and gravitational waves or matter fields have been achieved.