Abstract
In this paper, we will use a unitary gravitational action up to third-order of curvature with respect to the holographic a-theorem. In particular, its third-order term has a Weyl-cubed term. In this paper, we study this Weyl-cubed theory and find some of its exact classical solutions. We show that the theory admits conformally flat, Lifshitz, Schrödinger and also hyperscaling-violating backgrounds as the solutions of the equations of motion. Our analysis has been done for the pure Weyl-cubed gravity, Einstein plus Weyl-cubed term and gravity with matter.
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