Abstract
The Quadratic Gravity is an extension of Einstein's theory with additional terms in action that are quadratic combinations of the Riemann tensor and its contractions. These corrections are needed, for example, in perturbative quantum gravity.
We consider the family of Kundt spacetimes, which is defined in a purely geometrical way by admitting a shear-free, twist-free and expansion-free null geodesic congruence. In particular, we focus on the Kundt solutions without gyratonic terms, and we investigate the constraints imposed by the Quadratic Gravity field equations.
We investigate various special cases depending on the parameters in the theory, one of those cases being the Gauss-Bonnet gravity. The conditions for the metrics to be of various algebraic types are also studied.