Traversable wormholes in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> massive gravity
Takol Tangphati, Auttakit Chatrabhuti, Daris Samart, Phongpichit Channuie
Abstract
In this work, the study of traversable wormholes in $f(R)$ massive gravity with the function $f(R)=R+{\ensuremath{\alpha}}_{1}{R}^{n}$, where ${\ensuremath{\alpha}}_{1}$ and $n$ are arbitrary constants, is considered. We choose the shape function of the form $b(r)=r\mathrm{exp}(\ensuremath{-}\ensuremath{\alpha}(r\ensuremath{-}{r}_{0}))$ with $\ensuremath{\alpha}$ and ${r}_{0}$ being an arbitrary constant and a radius of the wormhole throat, respectively. Here $\ensuremath{\alpha}$ affects the radius of curvature of the wormhole. 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, $\mathrm{\ensuremath{\Phi}}=\text{constant}$, ${\ensuremath{\gamma}}_{1}/r$, $\mathrm{log}(1+{\ensuremath{\gamma}}_{2}/r)$ with ${\ensuremath{\gamma}}_{1}$ and ${\ensuremath{\gamma}}_{2}$ are arbitrary real constants. We also compute the volume integral quantifier to calculate the amount of the exotic matter near the constructed wormhole throat.