AdS black holes in Einstein-Kalb-Ramond gravity: Quantum corrections, phase transitions, and orbital dynamics

We investigate black hole dynamics in Einstein-Kalb-Ramond (EKR) gravity coupled with a global monopole, focusing on thermodynamic corrections, geodesic stability, and Lorentz symmetry breaking (LSB) effects. By deriving exact static, spherically symmetric solutions in Anti-de Sitter spacetime, we analyze how the non-minimal coupling between the Kalb-Ramond (KR) field and Ricci tensor induces LSB through a non-vanishing vacuum expectation value. Our semiclassical calculations of Hawking radiation via tunneling methods yield consistent temperature expressions, which we enhance with Generalized Uncertainty Principle corrections to capture quantum gravity effects at microscopic scales. We derive quantum modifications to thermodynamic quantities including entropy, internal energy, Helmholtz free energy, pressure, and heat capacity, revealing a phase transition induced by positive cosmological constant values that drives the system from thermodynamic instability to stability with increasing horizon radius. Our geodesic analysis, employing effective potential formalism and Lyapunov exponent calculations, demonstrates how LSB and global monopole contributions modify orbital dynamics, particularly near the black hole.