Zainab NazishCIIT/SP24-RMT-019/LHRDr. Abdul JawadLHR TP 100802026-06-022025https://repository.cuilahore.edu.pk/123456789/3982This thesis explores the thermodynamic behavior and stability of anti-de Sitter (AdS) black holes within the framework of bumblebee gravity, a theory in which Lorentz symmetry is spontaneously broken by a vector field. The study examines how the Lorentz-violating bumblebee parameter influences the event horizon structure and various thermodynamic properties in both standard and extended phase spaces. Thermal stability is analyzed through heat capacity and Helmholtz free energy. The results show that large bumblebee AdS black holes can simultaneously satisfy local and global stability conditions, with the stable regions strongly depending on the Lorentz-violating parameter. The research also investigates heat capacity at constant pressure in the extended phase space, where the cosmological constant is interpreted as thermodynamic pressure. In this case, the stability criteria are found not to be fulfilled, highlighting the significant role of Lorentz symmetry violation in black hole thermodynamics. In addition, the thesis studies the sparsity parameter and Hawking radiation emission rates for black hole solutions in bumblebee gravity using generalized entropy models, including Sharma–Mittal entropy and three-parameter entropy indices. The findings reveal that changing the sign of the cosmological constant significantly affects thermodynamic sparsity and entropy behavior. A negative cosmological constant reduces sparsity while increasing entropy, indicating a denser thermodynamic system. Conversely, a positive cosmological constant preserves higher thermodynamic sparsity. Furthermore, the emission spectrum becomes sharper for negative cosmological constant values, indicating enhanced low-energy emission within a confining AdS background, while a positive cosmological constant generally suppresses the emission rate.enDepartment of MathematicsSP24MathematicsBumblebee GravityBlack Hole ThermodynamicsModified EntropyDr. Abdul JawadThesis