Exact Gravitational Shock Wave Solution of Higher Order Theories

Abstract

We find an {\it exact} pp--gravitational wave solution of the fourth order gravity field equations. Outside the (delta--like) source this {\it not} a vacuum solution of General Relativity. It represents the contribution of the massive, $m=(-\beta {)}^{-1/2}$, spin--two field associated to the Ricci squared term in the gravitational Lagrangian. The fourth order terms tend to make milder the singularity of the curvature at the point where the particle is located. We generalize this analysis to $D$--dimensions, extended sources, and higher than fourth order theories. We also briefly discuss the scattering of fields by this kind of plane gravitational waves.

12 pages, REVTEX, Fully revised version. Amplitude of the wave computed. Discussion section added. Figure added. To appear in Phys. Rev. D

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• An exact self-consistent gravitational shock wave in semiclassical gravity
• Soft thermodynamics of gravitational shock wave
• A gravitational shock wave generated by a beam of null matter in quadratic gravity
• Some Classes of Gravitational Shock Waves from Higher Order Theories of Gravity
• Causality constraints in Quadratic Gravity