Publikace ÚTF

Since all Einstein spacetimes are vacuum solutions to quadratic gravity in four dimensions, in this paper
we study various aspects of non-Einstein vacuum solutions to this theory. Most such known solutions are of
traceless Ricci and Petrov type N with a constant Ricci scalar. Thus we assume the Ricci scalar to be
constant which leads to a substantial simplification of the field equations. We prove that a vacuum solution
to quadratic gravity with traceless Ricci tensor of type N and aligned Weyl tensor of any Petrov type is
necessarily a Kundt spacetime. This will considerably simplify the search for new non-Einstein solutions.
Similarly, a vacuum solution to quadratic gravity with traceless Ricci type III and aligned Weyl tensor of
Petrov type II or more special is again necessarily a Kundt spacetime. Then we study the general role of
conformal transformations in constructing vacuum solutions to quadratic gravity. We find that such
solutions can be obtained by solving one nonlinear partial differential equation for a conformal factor on
any Einstein spacetime or, more generally, on any background with vanishing Bach tensor. In particular, we
show that all geometries conformal to Kundt are either Kundt or Robinson–Trautman, and we provide some
explicit Kundt and Robinson–Trautman solutions to quadratic gravity by solving the above mentioned
equation on certain Kundt backgrounds.