Spherically symmetric solution of $f(R,\mathcal{G})$ gravity at low energy

Abstract

The weak-field and slow-motion limit of $f(R,\mathcal{G})$ gravity is developed up to $(v/c{)}^4$ order in a spherically symmetric background. Considering the Taylor expansion of a general function $f$ around vanishing values of $R$ and $\mathcal{G}$, we present general vacuum solutions up to $(v/c{)}^4$ order for the gravitational field generated by a ball-like source. The spatial behaviors at $(v/c{)}^2$ order are the same for $f(R,\mathcal{G})$ gravity and $f(R)$ gravity, and their corresponding real valued static behaviors are presented and compared with the one in general relativity. The static Yukawa-like behavior is proved to be compatible with the previous result of the most general fourth-order theory. At $(v/c{)}^4$ order, the static corrections to the Yukawa-like behavior for $f(R,\mathcal{G})$ gravity, $f(R)$ gravity, and the Starobinsky gravity are presented and compared with the one in general relativity.

14 latex files, 11 figures

References in corpus (14)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Low surface brightness galaxies rotation curves in the low energy limit of $R^n$ gravity : no need for dark matter?
• Limit to General Relativity in f(R) theories of gravity
• The Newtonian Limit of F(R) gravity
• Dark energy and dark matter as curvature effects
• Spherical symmetry in $f(R)$-gravity
• Ghosts, Instabilities, and Superluminal Propagation in Modified Gravity Models
• Dark matter and dark energy as a effects of Modified Gravity
• Ghost Constraints on Modified Gravity
• A general solution in the Newtonian limit of f(R)- gravity
• Starobinsky-type Inflation in Dynamical Supergravity Breaking Scenarios
• The Newtonian limit of metric gravity theories with quadratic Lagrangians
• The most general fourth order theory of Gravity at low energy
• Cosmological entropy and generalized second law of thermodynamics in $F(R,G)$ theory of gravity

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