Axially symmetric solutions in f(R)-gravity

TL;DR

This paper presents a method to derive axially symmetric solutions in f(R)-gravity using a complex coordinate transformation, extending techniques from General Relativity, and analyzes their physical properties.

Contribution

It introduces a novel approach combining Noether symmetries and Newman-Janis transformations to generate axially symmetric solutions in f(R)-gravity.

Findings

Successfully derived axially symmetric solutions from spherically symmetric ones.

Demonstrated the general applicability of the method with an explicit example.

Analyzed the physical characteristics of the obtained solutions.

Abstract

Axially symmetric solutions for f (R)-gravity can be derived starting from exact spherically sym- metric solutions achieved by Noether symmetries. The method takes advantage of a complex coordi- nate transformation previously developed by Newman and Janis in General Relativity. An example is worked out to show the general validity of the approach. The physical properties of the solution are also considered.