Study of Wormholes in Symmetric Teleparallel Theories of Gravity

Abstract: This thesis explores traversable wormhole (WH) solutions within symmetric teleparallel gravity and its extensions, including $f(Q)$ and $f(Q, T)$ gravity. Chapter I reviews WH geometry and properties, general relativity, and modified gravity's role in WH physics. Chapter II constructs WHs in $f(Q)$ gravity using dark matter profiles like Pseudo-Isothermal and Navarro-Frenk-White (NFW). For linear $f(Q)$ models, suitable redshift and shape functions satisfying the flare-out condition yield viable WHs, with the monopole charge $\eta$ driving Null Energy Condition (NEC) violation. The Volume Integral Quantifier (VIQ) method shows minimal exotic matter is needed. Nonlinear models like $f(Q) = Q + m Q^n$ fail to meet WH criteria. Chapter III studies $f(Q, T)$ gravity, where $Q$ and the trace $T$ of the energy-momentum tensor are coupled. WHs are examined under barotropic and anisotropic equations of state using forms like $f(Q, T) = \alpha Q + \beta T$ and $f(Q, T) = Q + \lambda_1 Q^2 + \eta_1 T$. NEC violations occur near the throat, indicating effective matter-geometry coupling. Tolman-Oppenheimer-Volkoff (TOV) analysis confirms equilibrium under suitable parameters. Chapter IV employs the MIT bag model in $f(Q, T)$ gravity, treating it as a source of exotic matter. Specific shape functions lead to WHs with NEC violation and TOV-based stability under radial perturbations. Chapter V considers WHs in $f(Q, T)$ gravity with noncommutative geometries inspired by string theory. Gaussian and Lorentzian smeared sources are used. Linear models yield analytical WH solutions, nonlinear ones are numerical. All satisfy the flare-out condition and exhibit NEC violation. Gravitational lensing analysis reveals distinguishable features from black holes. Chapter VI summarizes the results, emphasizing observational prospects in extended gravity frameworks.