Quasi-periodic oscillations in Letelier black holes within Kalb-Ramond gravity embedded in a uniform external magnetic field

Abstract

We investigate the dynamics of charged test particles around a Letelier black hole, i.e. a black hole surrounded by a cloud of strings (CoS), in Kalb-Ramond (KR) gravity, immersed in an external, asymptotically uniform magnetic field aligned with the symmetry axis. The geometry depends on the CoS parameter and on the Lorentz-violating KR parameter only through a single combination of the two, so that the two effects can compensate each other and the Schwarzschild metric is recovered when both parameters are equal. Because the spacetime is not Ricci flat, the Wald potential is not a solution of the Maxwell equations; we show that the regular source-free magnetic test field is given in closed form by a Gauss hypergeometric function of the radial coordinate, which reduces to the Wald solution in the Schwarzschild limit. Using this exact field we derive the equations of motion, the effective potential, the circular orbits, the innermost stable circular orbit (ISCO), representative escaping, captured and curled trajectories, and the orbital, radial and vertical epicyclic frequencies in closed form; all frequency expressions are cross-checked against direct numerical integration of the full equations of motion. Within the relativistic precession model, we perform a Markov chain Monte Carlo (MCMC) analysis of the twin-peak high-frequency quasi-periodic oscillations (QPOs) of GRO J1655-40, XTE J1550-564 and GRS 1915+105 for four nested models, complemented by nested sampling to compute Bayesian evidences and to weight the two (Larmor and anti-Larmor) magnetic modes of the posterior. The Schwarzschild model is excluded for GRO J1655-40 and XTE J1550-564, with a difference in the Akaike information criterion of about 110.