# Validation of Energy Conditions in Wormhole Geometry within Viable $f(R)$ Gravity

## TL;DR

This paper investigates wormhole geometries in $f(R)$ gravity, deriving specific solutions and analyzing energy conditions to identify regions where these conditions hold, thus contributing to the understanding of viable wormhole models.

## Contribution

It introduces a specific shape function and equation of state within $f(R)$ gravity to analyze energy conditions in wormholes, providing new insights into their viability.

## Key findings

- Identified spherical regions where energy conditions are satisfied.
- Derived the $f(R)$ function compatible with the wormhole geometry.
- Determined the range of throat radii satisfying energy conditions.

## Abstract

In this work, wormholes, tunnel like structures introduced by Morris \& Thorne \cite{Morris95}, are explored within the framework of $f(R)$ gravity. Using the shape function $b(r)=r_0\big(\frac{r}{r_0}\big)^\gamma$, where $0<\gamma<1$, and the equation of state $p_r=\omega\rho$, the $f(R)$ function is derived and the field equations are solved. Then null, weak, strong and dominated energy conditions are analyzed and spherical regions satisfying these energy conditions are determined. Furthermore, we calculated the range of the radius of the throat of the wormhole, where the energy conditions are satisfied.