Universal metrics are solutions of all possible higher order gravity theories simultaneously regardless to the form of their quantum corrections. Consequently, they are solutions of the full quantum gravity despite the fact that we do not known what the t heory precisely should be. At the present time, the research of universal metrics is at the very beginning. We plan to start a systematical study of universal metrics, their admissible algebraic types, relation to the classes of VSI and CSI spacetimes and find their explicit examples.
Using the recently developed generalizations of algebraic classification and the Newman-Penrose formalism to the case of arbitrary tensors on Lorentzian manifolds of arbitrary dimension, we also plan to generalize our metho d for finding classes of algebraically special exact solutions of quadratic gravity to more general higher order gravity theories such as the Lovelock theory. This approach will lead to new classes of exact solutions of these theories.