Abstract
Penrose [R. Penrose, The geometry of impulsive gravitational waves, in General Relativity, Papers in Honour of J. L. Synge, L. O'Raifeartaigh, ed., Clarendon Press, Oxford, 1972, pp. 101–115], – in a purely formal way – introduced a ‘discontinuous coordinate transformation’, which relates a continuous representation of the metric of impulsive pp-waves to a discontinuous one. On the basis of the invertibility concept for generalized functions developed recently by Erlacher [E. Erlacher, Inversion of Colombeau generalized functions, preprint (2010)], we show that this discontinuous coordinate transformation indeed represents an invertible generalized function in the appropriate sense.
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