Nonlinear Lagrangians and pp waves

From time to time modifications of Einstein's general theory of relativity have been considered the central feature of which, on a formal level, is the appearance in place of the Einstein Lagrangian R of a more general Lagrangian L. On physical grounds it is necessary for L to differ from R only by terms whose presence has no substantial observational consequences under 'ordinary' conditions. Here pp waves are considered, first as exact solutions of the vacuum equations generated by a family of inhomogeneous quadratic Lagrangians L*. Thereafter a much wider class of Lagrangians is contemplated, but the greater generality of this is only apparent since all such Lagrangians in effect reduce to L*. (author)