Geodesic structure, eikonal quasinormal modes and thermodynamic properties of a Schwarzschild-de Sitter-like black hole with global monopole in Bumblebee gravity

Abstract

We investigate the geodesic dynamics, eikonal quasinormal modes (QNMs), and extended phase space thermodynamics of a Schwarzschild-de Sitter-like black hole coupled with a global monopole in Bumblebee gravity. Our analysis reveals that spontaneous Lorentz symmetry breaking and topological defects modify the effective radial dynamics, leading to lower effective potential barriers and a reduced magnitude of the effective force. For null geodesics, higher monopole parameters expand the photon sphere and critical impact parameter, implying an enlarged black hole shadow, while mitigating dynamical instability. For massive particles, the stable circular orbit window narrows significantly as the Outermost Stable Circular Orbit (OSCO) shrinks, alongside a marked enhancement in perihelion precession. In addition, we examine the correspondence between the eikonal QNMs and the properties of null geodesics. The excellent agreement between the eikonal approximation and the WKB method for scalar and electromagnetic perturbations supports the validity of the correspondence for the spacetime under consideration. In the extended thermodynamic phase space, we evaluate the black hole as a holographic heat engine. We demonstrate that classical efficiency is mathematically blind to Lorentz violation; however, introducing a quantum-corrected modified entropy tightly couples the macroscopic work output to the symmetry-breaking framework. Ultimately, the necessity to respect the Carnot bound imposes a strict macroscopic constraint on the Lorentz-violating parameter, safeguarding the Second Law of Thermodynamics.