Traversable wormholes in $f(R)$ gravity with constant and variable redshift functions

Abstract

The present paper is aimed at the study of traversable wormholes in $f(R)$ gravity with a viable $f(R)$ function defined as $f(R)=R-\mu R_c\Big(\frac{R}{R_c}\Big)^p$, where $R$ is scalar curvature, $\mu$, $R_c$ and $p$ are constants with $\mu, R_c>0$ and $0<p<1$ \citep{Amendola}. The metric of wormhole is dependent on shape function $b(r)$ and redshift function $\phi(r)$ which characterize its properties, so the shape function and redshift function play an important role in wormhole modeling. In this work, the wormhole solutions are determined for (i) $\phi(r)=\frac{1}{r}$ and (ii) $\phi(r)=c$ (constant) with $b(r)=\frac{r}{exp(r-r_0)}$ \citep{godani1}. Further, the regions respecting the energy conditions are investigated.