Bertotti-Robinson solutions in five--dimensional quadratic gravity

We construct new solutions of five-dimensional quadratic gravity as direct products of a constant curvature two-surface with a solution of three-dimensional new massive gravity with constant scalar curvature. These solutions could represent near-horizon limits of five-dimensional asymptotically flat black strings or black rings. A number of these non-asymptotically flat solutions are themselves black strings or rings. A by-product of our analysis is the construction of new solutions of four-dimensional quadratic gravity obtained by toroidal reduction of the five-dimensional solutions with flat transverse space. These again include black strings or rings, and an $AdS_2\times T^2$ solution of $f(R)$ gravity for a specific relation between the model parameters.