Researchers have explored how spontaneous Lorentz symmetry breaking impacts scalar wave propagation and the thermodynamic behavior of anti-de Sitter (AdS) black holes within "bumblebee gravity" theory. This theory introduces a vector field that, by acquiring a vacuum expectation value, breaks Lorentz symmetry, a cornerstone of special and general relativity. The study focuses on static, spherically symmetric solutions, characterized by a dimensionless parameter $\ell > -1$ that globally rescales the black hole's radial geometry.