Causality and a-theorem Constraints on Ricci Polynomial and Riemann Cubic Gravities

Abstract

In this paper, we study Einstein gravity extended with Ricci polynomials and derive the constraints on the coupling constants from the considerations of being ghost free, exhibiting an $a$-theorem and maintaining causality. The salient feature is that Einstein metrics with appropriate effective cosmological constants continue to be solutions with the inclusion of such Ricci polynomials and the causality constraint is automatically satisfied. The ghost free and $a$-theorem conditions can only be both met starting at the quartic order. We also study these constraints on general Riemann cubic gravities.

Latex, 31 pages, typos corrected, comments and references added

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Cited by in corpus (5)

• Slowly rotating black holes in Einsteinian cubic gravity
• Holographic Studies of The Generic Massless Cubic Gravities
• Holographic (a,c)-charges and Their Universal Relation in d=6 from Massless Higher-order Gravities
• Higher-Curvature Gravity, Black Holes and Holography
• Aspects of three-dimensional higher-curvature gravities