# Non violation of energy conditions in wormholes modelling

## TL;DR

This paper investigates traversable wormholes with a specific shape function in $f(R)$ gravity, demonstrating conditions under which energy conditions are satisfied, thus avoiding the need for exotic matter.

## Contribution

It introduces a new shape function for wormholes in $f(R)$ gravity and analyzes energy conditions across various parameter choices, showing non-violation of energy conditions.

## Key findings

- Energy conditions are satisfied for certain parameter ranges.
- The equation of state parameter indicates anisotropic matter.
- Wormholes can exist without exotic matter in this model.

## Abstract

Morris \& Thorne \cite{morris1} proposed geometrical objects called traversable wormholes that act as bridges in connecting two spacetimes or two different points of the same spacetime. The geometrical properties of these wormholes depend upon the choice of the shape function. In literature, these are studied in modified gravities for different types of shape functions. In this paper, the traversable wormholes having shape function $b(r)=\frac{r_0\tanh(r)}{\tanh(r_0)}$ are explored in $f(R)$ gravity with $f(R)=R+\alpha R^m-\beta R^{-n}$, where $\alpha$, $\beta$, $m$ and $n$ are real constants. For different values of constants in function $f(R)$, the analysis is done in various cases. In each case, the energy conditions, equation of state parameter and anisotropic parameter are determined.