Wormhole solutions in $f(R)$ Gravity

TL;DR

This paper explores traversable wormhole solutions within $f(R)$ gravity, presenting three models with specific shape functions and analyzing their behaviors based on a parameter-dependent $f(R)$ function.

Contribution

It introduces new wormhole solutions in $f(R)$ gravity with models based on physically motivated shape functions and a novel parameter-dependent $f(R)$ form.

Findings

Three wormhole models with distinct behaviors are analyzed.

The $f(R)$ functions depend on a parameter $\alpha$, affecting the solutions.

The models demonstrate the viability of wormholes in modified gravity theories.

Abstract

In this work, we have studied the traversable wormholes geometry in $f(R)$ theory gravity, where $R$ be the Ricci scalar. The wormhole solution for some assumed $f(R)$ functions have been presented. The assumption of $f(R)$ is based on the fact that its behaviour changed with an assumed parameter $\alpha$ rather than the deceleration parameter. Three models are presented based on the physically motivated shape function and their behaviours are studied.