Exploring Wormholes in Modified Theories of Gravity

Abstract: This thesis investigates traversable wormhole spacetimes in modified theories of gravity, where the matter at the wormhole throat is described by an anisotropic energy-momentum tensor. Wormhole solutions are constructed in the context of $f(Q)$ gravity under various equations of state, and their physical viability and stability are thoroughly examined. The influence of the Generalized Uncertainty Principle (GUP) on Casimir wormholes is also analyzed, emphasizing the role of the GUP parameter in shaping wormhole geometry in $f(Q)$ gravity. Additionally, the study investigates the observational aspects of wormholes, such as their shadow profiles and deflection angles in the presence of dark matter. The work is further extended to four-dimensional Einstein-Gauss-Bonnet (EGB) gravity, where the effects of dark matter models and the Gauss-Bonnet coupling parameter on the energy conditions are evaluated. Various physical properties of the wormholes, including the complexity factor, active gravitational mass, and total gravitational energy, are also discussed.