Wormhole thermodynamics in matter-geometry coupled theory: Implications of pseudo-isothermal profile and complexity factor

The objective of this article is to explore the existence of traversable wormholes possessing the pseudo-isothermal profile in modified $f(R,T)$ gravity. We utilize the Morris-Thorne spacetime to define the wormhole structure and develop anisotropic gravitational equations for a linear modified gravity model. Our analysis involves deriving the shape functions by taking into account both constant and variable redshift functions. These shape functions adhere to the required conditions and create a connection between two asymptotically flat regions of spacetime. For each of the two cases, we analyze energy conditions whose satisfaction ensures the existence of wormholes without the necessity for exotic matter. Furthermore, we evaluate the active gravitational mass, complexity factor and volume integral quantifier for the proposed solutions. It is revealed that all these quantities gain positive value at the wormhole's throat. Afterwards, a detailed stability analysis of the developed models is performed through certain criteria. We also analyze the thermodynamic behavior, focusing on the variation of entropy and its implications for the wormhole geometry. Our findings suggest that the pseudo-isothermal wormhole geometry exists in the context of the considered matter-geometry coupled modified theory.