# Vacuum Solutions of FRW and Axially Symmetric space-time in f(R) Theory of Gravity

## TL;DR

This paper derives vacuum solutions for FRW and axially symmetric spacetimes within f(R) gravity, analyzing their physical behavior and Ricci scalar functions to understand their cosmological implications.

## Contribution

It provides new vacuum solutions in f(R) gravity for both FRW and axially symmetric models, with assumptions linking scale factors and scalar fields.

## Key findings

- Solutions describe vacuum spacetime geometries in f(R) gravity
- Physical parameters analyzed for model behavior
- Ricci scalar functions characterized for these models

## Abstract

In the present paper an attempt has been made to study the spatially homogeneous and isotropic FRW model and axially symmetric spacetime in f(R) theory of gravity. We have obtained the solutions of the field equations in vacuum. To find the solutions of axially symmetric space-time we have assumed the relation between scale factor and scalar field and also we considered that scalar expansion ({\theta}) in the model is proportional to shear scalar ({\sigma}). The physical behavior for both models have been discussed by using physical parameters. The function of Ricci scalar is investigated for these models. Key words: f(R) theory of gravity, FRW universe, Axially symmetric space-time.