Abstract
In this paper and the subsequent one, the quantum scattering of particles by a gravitational shock wave (GSW) is computed within the framework of string theory. The exact string equations of motion and constraints in the GSW background are reviewed for the light-cone gauge. In addition, the ambiguity in the solution for the longitudinal coordinate is solved. The light-cone solution is generalized to an arbitrary covariant gauge. This general solution turns out to be completely explicit and not much more involved than the solution for the light-cone gauge. The extension of the string solution to the case of a GSW generated by an arbitrary ultrarelativistic source is also presented.
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