Minimal Extension of Einstein's Theory: The Quartic Gravity

Abstract

We study structure of solutions of the recently constructed minimal extensions of Einstein's gravity in four dimensions at the quartic curvature level. The extended higher derivative theory, just like Einstein's gravity, has only a massless spin-two graviton about its unique maximally symmetric vacuum. The extended theory does not admit the Schwarzschild or Kerr metrics as exact solutions, hence there is no issue of Schwarzschild type singularity but, approximately, outside a source, spherically symmetric metric with the correct Newtonian limit is recovered. We also show that for all Einstein space-times, square of the Riemann tensor (the Kretschmann scalar or the Gauss-Bonnet invariant) obeys a non-linear scalar Klein-Gordon equation.

12 pages, 2 figures, typos corrected, version to appear in PRD

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• Aspects of general higher-order gravities
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• On black holes in higher-derivative gravities
• All higher-curvature gravities as Generalized quasi-topological gravities
• Universality of squashed-sphere partition functions
• Universal Structure of Covariant Holographic Two-Point Functions In Massless Higher-Order Gravities
• Unimodular Gravity Traversable Wormholes
• Holographic Studies of The Generic Massless Cubic Gravities
• Constraints on Cubic and $f(P)$ Gravity from the Cosmic Chronometers, BAO & CMB datasets : Use of Machine Learning Algorithms
• Entropy in Born-Infeld Gravity
• Higher order gravities and the Strong Equivalence Principle
• Higher-Curvature Gravity, Black Holes and Holography
• Inflation in pure gravity with only massless spin-2 fields
• Anomaly Induced Inflation in the Minimal Quartic Extension of Einstein's Gravity
• Aspects of three-dimensional higher-curvature gravities