Aspects of general higher-order gravities

Abstract

We study several aspects of higher-order gravities constructed from general contractions of the Riemann tensor and the metric in arbitrary dimensions. First, we use the fast-linearization procedure presented in arXiv:1607.06463 to obtain the equations satisfied by the metric perturbation modes on a maximally symmetric background in the presence of matter and to classify $\mathcal{L}($Riemann$)$ theories according to their spectrum. Then, we linearize all theories up to quartic order in curvature and use this result to construct quartic versions of Einsteinian cubic gravity (ECG). In addition, we show that the most general cubic gravity constructed in a dimension-independent way and which does not propagate the ghost-like spin-2 mode (but can propagate the scalar) is a linear combination of $f($Lovelock$)$ invariants, plus the ECG term, plus a New ghost-free gravity term. Next, we construct the generalized Newton potential and the Post-Newtonian parameter $\gamma$ for general $\mathcal{L}($Riemann$)$ gravities in arbitrary dimensions, unveiling some interesting differences with respect to the four-dimensional case. We also study the emission and propagation of gravitational radiation from sources for these theories in four dimensions, providing a generalized formula for the power emitted. Finally, we review Wald's formalism for general $\mathcal{L}($Riemann$)$ theories and construct new explicit expressions for the relevant quantities involved. Many examples illustrate our calculations.

83 pages, 3 figures, 4 tables; v2: minor modifications to match published version, references added

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• Holographic Studies of The Generic Massless Cubic Gravities
• Minisuperspace Quantum Cosmology in Metric and Affine Theories of Gravity
• On the viability of the evolution of the universe with Geometric Inflation
• The extremal Kerr entropy in higher-derivative gravities
• A unified geometric description of the Universe: from inflation to late-time acceleration without an inflaton nor a cosmological constant
• Slowly rotating black holes in Quasi-topological gravity
• CFT correlators from shape deformations in Cubic Curvature Gravity
• Holographic (a,c)-charges and Their Universal Relation in d=6 from Massless Higher-order Gravities
• Higher order gravities and the Strong Equivalence Principle
• Universal renormalization procedure for higher curvature gravities in D$\le$5
• Higher-Curvature Gravity, Black Holes and Holography
• Aspects of three-dimensional higher-curvature gravities
• $f(R)$ Gravity Effects on Charged Accelerating AdS Black Holes using Holographic Tools