Exact gyratons in higher and infinite derivative gravity

We study solutions describing spinning null sources called gyratons in generic theories of gravity with terms that are quadratic in curvature and contain an arbitrary number of covariant derivatives. In particular, we show that the properties of pp waves of the algebraic type III allow for extreme simplification of the field equations. It turns out that the resulting differential equations are exactly solvable due to partial decoupling and linearity of the equations. This is demonstrated explicitly by finding axially symmetric gyraton solutions in Stelle's fourth derivative gravity and the nonlocal gravity with an infinite number of derivatives.