A study of cylindrically symmetric solutions in f(R, phi , X) theory of gravity

Adnan Malik,Ayesha Nafees,Muhammad Naeem Butt,Akram Ali

doi:10.1140/epjc/s10052-022-10135-0

Abstract

In this article, we aim to investigate some cylindrically symmetric solutions in a very well known modified theory named as f(R, phi , X) theory of gravity, where the terms R, phi and X are clarified as Ricci Scalar, scalar potential, and kinetic term respectively. For this purpose, we consider the cylindrically symmetric space-time to discuss the cylindrical solutions in some realistic regions. We further discuss six distinct cases of exact solutions using the field equations of f(R, phi , X) modified theory of gravity. Furthermore, we set some suitable values of U_0 and alpha in f(R, phi , X)=R+alpha R^2 - V(phi )+ X for the investigation of well-known Levi–Civita and cosmic string solutions. The Energy conditions are also investigated for all different cases and observed that null energy conditions are violated, which is the indication of the existence of cylindrical wormholes.

Highlights

According to the Big bang theory, a massive blast from a single point of uncountable density was the reasoning behind the existence of our universe
The reason defined beyond this accelerating expansion is some kind of matter and energy known as Dark Matter (DM) and Dark Energy (DE) [4,5,6,7,8,9,10,11]
It can be noticed that Null Energy Condition (NEC), Weak Energy Condition (WEC), Strong Energy Condition (SEC), and Dominant Energy Condition (DEC) are satisfied due to positive and increasing trends of pressure, as seen in Figs. 22, 23 and 24

Summary

Introduction

According to the Big bang theory, a massive blast from a single point of uncountable density was the reasoning behind the existence of our universe. Shamir and Zahid investigated the exact solutions of cylindrically symmetric space-time in the background of f (R) theory of gravity. Azadi et al [32] studied the static cylindrically symmetric vacuum solutions in Weyl coordinates in the context of the metric f (R) theories of gravity. Houndjo et al [34] investigated the static cylindrically symmetric vacuum solutions in Weyl coordinates in the framework of f (T ) theory of gravity, where T is the torsion scalar. Shamir and Malik considered this theory and investigated some exact solutions using the different equations of state parameters [39] Bahamonde, along with his collaborators [40] investigated new exact spherically symmetric solutions in f (R, φ, X ) modified gravity by Noether’s symmetry approach. We use ψ ≡ ψ(r ), χ ≡ χ (r ) and ζ ≡ ζ (r )

Analysis of energy conditions

Comparison

Levi–Civita solution

Cosmic string case

Conclusion