Spherically Symmetric Solutions to Fourth-Order Theories of Gravity

Abstract

Gravitational theories generated from Lagrangians of the form f(R) are considered. The spherically symmetric solutions to these equations are discussed, paying particular attention to features that differ from the standard Schwarzschild solution. The asymptotic form of solutions is described, as is the lack of validity of Birkhoff's theorem. Exact solutions are presented which illustrate these points and their stability and geodesics are investigated.

arXiv comment10 pages, published version

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• Some static spherically symmetric interior solutions of $f(R)$ gravity
• Spherical inhomogeneous solutions of Einstein and scalar-tensor gravity: a map of the land
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• A Geometrical Approach to Strong Gravitational Lensing in f(R) Gravity
• An analysis of the Sultana-Dyer cosmological black hole solution of the Einstein equations
• Searching for dynamical black holes in various theories of gravity
• New inhomogeneous universes in scalar-tensor and f(R) gravity
• Traversable Morris-Thorne-Buchdahl wormholes in quadratic gravity
• R^n gravity and the chameleon
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• Exact Friedmann Solutions in Higher-Order Gravity Theories
• General properties of $\mathbf{f}(\mathbf{R})$ gravity vacuum solutions
• Conformally Flat Collapsing Stars in f (R) gravity
• Clifton's spherical solution in f(R) vacuo harbours a naked singularity
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• Extended galactic rotational velocity profiles in $f(R)$ gravity background
• Symmetry of Brans-Dicke gravity as a novel solution-generating technique
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• Is gravitational collapse possible in $f(R)$ gravity?
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• Astrophysical black holes in screened modified gravity
• Unified $f(R)$ gravity at local scales
• Dynamical apparent horizons in inhomogeneous Brans-Dicke universes
• The future of gravitational theories in the era of the gravitational wave astronomy
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• f(R) Quantum Cosmology
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• The 1+1+2 formalism for Scalar-Tensor gravity
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• New effective theories of gravitation and their phenomenological consequences
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