Geodesic equations in the weak field limit of general $f(R)$ gravity theory

Abstract

In our work we presented the modified field equations generated by action with unspecified function $f(R)$. Assuming spherical symmetry, we used the corresponding static Schwarzschild-like metric in the weak field limit. Also we considered geodesic equations of motion describing orbits and orbital speeds which can be measured in galactic environment. We solved geodesic equations in the case of a power-law $f(R)$ theories, that is we set $f(R)=f_{0n} R^n$.