Traversable wormholes in $f(R)$-massive gravity

Abstract

In this work, the study of traversable wormholes in $f(R)$-massive gravity with the function $f(R)=R+{\alpha }_1{R}^n$, where ${\alpha }_1$ and $n$ are arbitrary constants, is considered. We choose the modified shape function $b(r)$. We consider a spherically symmetric and static wormhole metric and derive field equations. Moreover, we visualize the wormhole geometry using embedding diagrams. Furthermore, we check the null, weak, dominant and strong energy conditions at the wormhole throat with a radius $r_0$ invoking three types of redshift functions, $\Phi =\mathrm{constant},{\gamma }_1/r,\log (1+{\gamma }_2/r)$ with ${\gamma }_1$ and ${\gamma }_2$ are arbitrary real constants. We also compute the volume integral quantifier to calculate the amount of the exotic matter near the constructed wormhole throat.

v2: 24 pages, many figures, 3 tables, the title changed reflecting a major revision