Casimir wormhole solutions in 𝑓(𝑅,𝑚 ) gravity

Abstract

In this paper, we study the Casimir effect on the wormhole geometry in 𝑓(𝑅,𝑚 ) gravity. We derive the field equations for the generic 𝑓(𝑅,𝑚 ) function by assuming static and spherically symmetric Morris–Thorne wormhole metric. Then we consider two non-linear 𝑓(𝑅,𝑚 ) models, specifically, 𝑓(𝑅,𝑚 ) = 𝑅 2 + 𝛽 𝑚 and 𝑓(𝑅,𝑚 ) = 𝑅 2 +(1+𝛼𝑚 )𝑚 where 𝛼 and 𝛽 are free parameters. We derive the shape functions for wormholes by utilizing the Casimir effect and examining their existence. Subsequently, we analyse the obtained wormhole solutions for each scenario, assessing the energy conditions at the wormhole throat with a radius of 𝑟0 . Our findings reveal that for some arbitrary quantities, there is a violation of classical energy conditions at the wormhole throat. Additionally, we delve into the behaviour of the equation of state (EoS) for each case. Furthermore, we explore the stability of the Casimir effect wormhole solutions by employing the generalized Tolman–Oppenheimer–Volkoff (TOV) equation. Finally, we utilize the volume integral quantifier to determine the amount of exotic matter required near the wormhole throat for both models.