Type III and N universal spacetimes

What is it about?

In general, it is very difficult to find exact solutions of generalized theories of gravity. However, it is known that some particular exact solutions of Einstein's gravity, such as pp-waves, are "immune" to corrections - they are also exact vacuum solutions of all gravities with the Lagrangian constructed from the metric, the Riemann tensor and its derivatives. In this paper, we start a study of such "universal" spacetimes and prove several results about their geometric properties.

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Why is it important?

In this paper, we start a systematic study of universal spacetimes. This leads to classes of exact vacuum solutions of all generalized gravities (with the general form of the Lagrangian given above) and classical solutions to string theory. For type N, we obtained simple geometric necessary and sufficient conditions for universality. We also find a class of type III universal spacetimes and formulate a simple necessary condition for all universal spacetimes in terms of curvature invariants.