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Axially symmetric static vacuum exact solution (ASSVES) in Weyl coordinatesare studied in $f(R)$ theories of gravity. In particular, we obtain a generalexplicit expression for the dependence between $df(R)/dR$ and the $r$ and $z$coordinates and then the corresponding explicit form of $f(R)$ is obtained.Next, we present in detail the explicit solution of the modified fieldequations corresponding to the Newtonian potential due to a punctual massplaced at the origin of coordinates and also the Schwarzschild solution to themodified field equations.

Exact solutions in metric $f(R)$-gravity for static axisymmetric spacetime