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

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Axially symmetric static vacuum exact solution (ASSVES) in Weyl coordinates are studied in f(R) theories of gravity. In particular, we obtain a general explicit 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 field equations corresponding to the Newtonian potential due to a punctual mass placed at the origin of coordinates and also the Schwarzschild solution to the modified field equations.