A comparative study of wormhole geometries under two different modified gravity formalism

Abstract In the current article, we discuss the wormhole geometries in two different gravity theories, namely $$\texttt{F}(\texttt{Q, T})$$ F ( Q , T ) gravity and $$\texttt{F}(\texttt{R, T})$$ F ( R , T ) gravity. In these theories, $$\texttt{Q}$$ Q is called a non-metricity scalar, $$\texttt{R}$$ R stands for the Ricci scalar, and $$\texttt{T}$$ T denotes the trace of the energy–momentum tensor (EMT). The main goal of this study is to comprehensively compare the properties of wormhole solutions within these two modified gravity frameworks by taking a particular shape function. The conducted analysis shows that the energy density is consistently positive for wormhole models in both gravity theories, while the radial pressure is positive for $$\texttt{F}(\texttt{Q, T})$$ F ( Q , T ) gravity and negative in $$\texttt{F}(\texttt{R, T})$$ F ( R , T ) gravity. Furthermore, the tangential pressure shows reverse behavior in comparison to the radial pressure. By using the Tolman-Oppenheimer-Volkov (TOV) equation, the equilibrium aspect is also described, which indicates that hydrostatic force dominates anisotropic force in the case of $$\texttt{F}(\texttt{Q, T})$$ F ( Q , T ) gravity theory, while the reverse situation occurs in $$\texttt{F}(\texttt{R, T})$$ F ( R , T ) gravity, i.e., anisotropic force dominates hydrostatic force. Moreover, using the concept of the exoticity parameter, we observed the presence of exotic matter at or near the throat in the case of $$\texttt{F}(\texttt{Q, T})$$ F ( Q , T ) gravity while matter distribution is exotic near the throat but normal matter far from the throat in $$\texttt{F}(\texttt{R, T})$$ F ( R , T ) gravity case. In conclusion, precise wormhole models can be created with a potential NEC and DEC violation at the throat of both wormholes while having a positive energy density, i.e., $$\rho >0$$ ρ > 0 .