New Wormhole Solutions in a Viable $f(R)$ Gravity Model

Abstract: Traversable wormhole solutions in General Relativity require exotic matter sources that violate the null energy condition (NEC), and such behavior maybe avoided in modified gravity. In this study, we analyze the energy conditions for static, spherically symmetric traversable Morris-Thorne wormholes in a recently proposed viable $f(R)$ gravity model. We numerically analyze solutions considering both constant and variable redshift functions, and present wormhole space-times respecting the NEC, supported by a phantom energy-like equation of state for the source. Moreover, we analyze the stability of the space-times using the generalized Tolman-Oppenheimer-Volkov equation. We demonstrate the effects of certain parameters in the $f(R)$ model in determining energy condition violations, and establish that stable wormholes can be formulated only at the expense of violating the NEC.