Energy Constraints for Evolving Spherical and Hyperbolic Wormholes in $f(R,T)$ Gravity

The primary objective of this article is to study the energy condition bounds for spherical and hyperbolic wormholes in well-known $f(R,T)$ theory of gravity. For this purpose, we formulate the field equations for spherically and pseudospherically geometries using anisotropic matter and linear form of generic function $f(R,T)$. By imposing different conditions on radial and tangential pressures or by adopting some known choices for red shift and shape functions, we present the graphical analysis of energy conditions for both spherically and pseudospherically symmetric wormholes. It is seen that energy density for spherically symmetric wormhole is always positive for $\lambda>-4\pi$ and $\lambda<-8\pi$, while the energy conditions for radial pressure are negative at throat. Likewise, in case of pseudospherically symmetric wormhole, it is observed that energy density is always positive for negative $\lambda$, however conditions based on radial pressure may be positive or negative for the considered different cases.