Exact Gravitational Shock Wave Solution Of Higher Order Theories

We find an exact pp--gravitational wave solution of the fourth order gravity field equations. The sourceless version of it is not a vacuum solution of General Relativity. It represents the contribution of the massive, m = (\Gammafi) \Gamma1=2 , spin-- two field associated to the Ricci squared term in the gravitational Lagrangian. We generalize this analysis to D--dimensions, extended sources, and higher than fourth order theories. 04.50.+h, 04.20.Jb, 04.30.-w Typeset using REVT E X Present Address. Electronic Address: lousto@mail.physics.utah.edu I. INTRODUCTION Higher order theories of gravity are the generally covariant extension of General Relativity when one considers in the Lagrangian nonlinear terms in the curvature. The field equations derived by variation of this Lagrangian contain derivatives of the metric of an order higher than the second (except for the Lovelock's Lagrangian constructed from the D-dimensional extension of four dimensional invariants [1]). Historical..