Rotating Black Hole Solutions in f(R)-Gravity

We present a strategy to get axially symmetric solutions in f(R) gravity by starting from spherically symmetric space-times. To do so, we assume the validity of a complex coordinate transformation, which acts on the spherically symmetric metric and permits one to infer the corresponding f(R) modification. The consequences of this recipe are here described, giving particular emphasis to define a class of compatible axially symmetric solutions, which fairly well describes the motion in cylindrical geometries in the field of f(R), in two different classes of coordinates. We demonstrate that our approach is general and may be applied for several cases of interest. We also show that our treatment is compatible with the standard approach of general relativity, evaluating the motion of a freely falling particle in the context of our metric.