Lorentz-violating signatures in quasi-periodic oscillations from a magnetised Kalb-Ramond black hole

Abstract

We investigate the dynamics of charged particles around a Schwarzschild-like black hole sourced by a Kalb-Ramond field and immersed in a uniform external magnetic field. The Kalb-Ramond field introduces a Lorentz violation parameter $l$ that modifies the spacetime geometry, while the magnetic field profoundly influences the trajectories through the Lorentz force, leading to a rich variety of orbital behaviours including curled (epicyclic) motion and dramatic transitions between distinct energy boundary configurations. We derive the full equations of motion, the effective potential, and the fundamental frequencies of quasi-periodic oscillations, and perform a comprehensive Monte Carlo Markov Chain (MCMC) analysis using observational data from the microquasars GRO 1655-40, XTE 1550-564, and GRS 1915+105. The pure Schwarzschild model is statistically ruled out for all three sources. For GRO 1655-40 and XTE 1550-564, only the combined effect of the magnetic field and Lorentz violation yields statistically robust models, with best-fit values $\mathcal{B}\sim 0.03$-$0.04$ and $l\sim 0.08$--$0.10$. Remarkably, for GRS 1915+105, the most massive object in our sample, the Lorentz violation parameter alone is sufficient to model the QPO frequencies, yielding an optimal fit with $ΔAIC = ΔBIC = 0$. Across all three objects, a clear trend emerges: the required value of $l$ decreases as the mass of the astrophysical object increases, suggesting a mass-dependent scaling of the Kalb-Ramond parameter. These findings establish the combined KR and magnetic field framework as a viable and statistically robust scenario for modeling QPOs in microquasars, and indicate that Lorentz-violating modifications to gravity may leave observable imprints in the strong-field regime, offering new avenues for testing quantum-gravity phenomenology with current and next-generation X-ray missions.