Topological thermodynamics and observable signatures of charged black holes in modified gravity

Abstract

This study investigates the thermodynamic topology of charged black holes within a Lorentz symmetry violation framework, examining how key parameters influence the distribution and nature of topological charges. By parametrically examining the black hole, we found two distinct topological charges, which sum to zero, indicating Reissner-Nordstr & ouml;m phase transitions in the black hole system. Our analysis of charged black holes with Kalb-Ramond field modifications reveals consistent topological patterns that align with established Reissner-Nordstr & ouml;m thermodynamic behaviors. The investigation of photon sphere topology demonstrates discrete topological charges that depend on orientation while maintaining fixed total charge across parameter variations. These findings illuminate the intricate relationship between thermodynamic topology and gravitational structures, advancing the classification and stability analysis of black holes subject to Lorentz symmetry violation. Additionally, we analyze vertical and azimuthal frequencies alongside periastron precession rates in charged Kalb-Ramond black hole spacetimes. Our results show that electric charge enhances oscillation frequencies and precession peaks, while Kalb-Ramond coupling mitigates these effects by reducing oscillation rates and precession in the strong-field regime. These modulations are most pronounced near the innermost stable circular orbit and diminish at larger radii, confirming that Kalb-Ramond corrections are localized to the near-horizon region. Such characteristic signatures in quasi-periodic oscillations and orbital precession provide valuable observational probes for testing theoretical extensions to General Relativity that incorporate electromagnetic and Kalb-Ramond fields.