Stability analysis of wormhole solutions in f(Q) gravity utilizing Karmarkar condition with radial dependent redshift function

Abstract

In this work, we examine the properties of wormhole (WH) solutions in the context of modified $f\left(Q\right)$ gravity. The shape function (${\xi }_S\left(r\right)$) and redshift function ($\zeta \left(r\right)$) are crucial in wormhole modeling since they determine the metric of a wormhole and define its attributes. The investigation provides the interaction between $f\left(Q\right)$ gravity features and gravitational effects, guaranteeing insights into potential wormhole configurations. Subsequently, we have looked at the behavior of energy conditions and the fundamental properties of WHs. Additionally, the volume integral quantifier ($\mathrm{V\; IQ}$) is addressed, providing insight into the quantity of exotic matter needed in the vicinity of the wormhole throat. Furthermore, the stability of the WH solutions in both cases is examined using the Tolman–Oppenheimer–Volkoff (TOV) equation where it is evident that both WH solutions meet the equilibrium requirements. Both cases ensures the real-world acceptability of WH solutions due to the rising nature of active gravitational mass ($M_{active}$). Our findings contribute to the current discussion about alternative gravity theories and exotic spacetime geometries.