Exact Solutions in Weyl-Cubed Gravity

Abstract

A unitary gravitational action up to third order of curvature in which respects to the holographic $a-$theorem has been constructed in \cite{myers}. In particular, its third order term is just the Weyl-cubed term in four dimensions. In this paper, we study this theory and find some its exact classical solutions. We show that the theory admits conformally flat, Lifshitz, Schrödinger and also hyperscaling-violating backgrounds as the solutions of equations of motion. Our analysis has been done for the pure Weyl-cubed gravity, Einstein plus Weyl-cubed term and gravity with matter.

16 pages, no figure, Refrences added

References in corpus (12)

• Quantum Gravity at a Lifshitz Point
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Seeing a c-theorem with holography
• Non-relativistic holography
• A new cubic theory of gravity in five dimensions: Black hole, Birkhoff's theorem and C-function
• AdS and Lifshitz Black Holes in Conformal and Einstein-Weyl Gravities
• On higher derivative gravity, c-theorems and cosmology
• Hyperscaling Violating Solution in Coupled Dilaton-Squared Curvature Gravity
• Thermodynamics of nonlinear charged Lifshitz black branes with hyperscaling violation
• Towards the Cardy formula for hyperscaling violation black holes
• Hyperscaling-violating Lifshitz Solutions in Cubic Gravity