Contents

128 9 Invariants and the characterization of geometriesAs yet, this method has limitations. It does not so far give a completealgorithm for all possible limits, due to complications like the singularrelation of canonical frames for different Petrov types and the absence ofa complete classification of the derivatives for all cases; it assumes thatthe limit is a four-dimensional space-time (limits which become singularor shock hypersurfaces, representing shells or impulsive waves that can beboundaries of regions of other space-times, are not covered by this techniquethough examples have been given in the literature, e.g. Aichelburgand Sexl (1971), Ferrariand Pendenza (1990), Hotta and Tanaka (1993),Balasin and Nachbagauer (1996)); it does not give the coordinate transformationfor coordinates which are ignorable in the limiting space-time;and it does not ensure that the limit is global.