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.

arXiv comment14 latex files, 11 figures

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• Multipole analysis for linearized $f(R)$ gravity with irreducible Cartesian tensors
• The gravitational field outside a spatially compact stationary source in a generic fourth-order theory of gravity
• Scale-Invariant Bounce Cosmology in Weyl f(Q) Gravity with Quintom Signature
• Late-Time Cosmic Acceleration in Ricci-Gauss-Bonnet Gravity via Gradient Descent Optimization