Geodesic structure, perturbative dynamics and thermal properties of black hole in Kalb–Ramond gravity

In this work, we explored the dynamics of black holes within the framework of Kalb–Ramond gravity, emphasizing the effects of spontaneous Lorentz symmetry breaking on their perturbative and thermodynamic properties. Starting with a modified spherically symmetric black hole solution, we derived and analyzed the spin-dependent Regge–Wheeler potentials for scalar, vector, and tensor perturbations, uncovering significant deviations from the Schwarzschild black hole due to the Lorentz symmetry-breaking parameter. Our findings revealed that the parameter strongly influences the stability of the black hole and the propagation of perturbative modes. Additionally, we calculated GFs to investigate the transmission coefficients of black hole radiation and demonstrated their dependence on both the spin of the fields and the symmetry-breaking effects. Thermodynamic analyses showed modifications to the temperature, entropy, and specific heat, which highlighted the critical role of Lorentz symmetry-breaking effects on black hole stability. Furthermore, we discussed the area quantization of the black hole horizon, revealing its direct dependence on the symmetry-breaking parameter and providing insights into the quantum nature of black holes. These results collectively enrich our understanding of black hole physics under modified gravity theories and offer potential observational implications.