From Clifton-Barrow spherically symmetric to axially symmetric solution in f(R)-gravity

TL;DR

This paper extends Clifton's spherical f(R)-gravity solution to axially symmetric cases by applying the Newman-Janis algorithm, demonstrating a method to generate new solutions in modified gravity theories.

Contribution

It introduces a novel application of the Newman-Janis algorithm to f(R)-gravity, deriving axially symmetric solutions from known spherical solutions.

Findings

Successfully derived axially symmetric solutions in f(R)-gravity.

Demonstrated the applicability of the Newman-Janis algorithm beyond General Relativity.

Provided a new method for exploring rotating solutions in modified gravity theories.

Abstract

Starting from Clifton's spherical static solution for f(R)-gravity we can derive axial symmetric solutions using a methods that takes the advantage of a complex coordinate transformation. The new solutions are generated by applying the Newman-Janis algorithm previously used to transform any static spherically symmetric into axially metric in General Relativity