General relativity (GR) theory modifications include different scalar, vector, and tensor fields with non-minimal gravitational coupling. Kalb–Ramond (KR) gravity is a modified theory formulated based on the presence of the bosonic field. One astrophysical way to test gravity is by studying the motion of test particles in the spacetime of black holes (BHs) using observational data. In the present work, we aimed to test KR gravity through theoretical studies of epicyclic frequencies of particle oscillations using quasi-periodic oscillation (QPO) frequency data from microquasars. First, we derive equations of motion and analyze the effective potential for circular orbits. Also, we studied the energy and angular momentum of particles corresponding to circular orbits. In addition, we analyze the stability of circular orbits. It is shown that the radius of the innermost stable circular orbits is inversely proportional to the KR parameter. We are also interested in how the energy and angular momentum of test particles at ISCO behave around the KR BHs. We found that the Keplerian frequency for the test particles in KR gravity is the same as that in GR. Finally, we study the QPOs by applying epicyclic oscillations in the relativistic precession (RP), warped disc (WD), and epicyclic resonance (ER) models. We also analyze QPO orbits in the resonance cases of upper and lower frequencies 3:2, 4:3, and 5:4 in the QPO as mentioned above models. We obtain constraints on the KR gravity parameter and BH mass using a Monte Carlo Markov Chain simulation in the multidimensional parameter space for the microquasars GRO J1655-40 & XTE J1550-564, M82 X-1, and Sgr A*.

Studying black holes in alternative gravitational frameworks is crucial for understanding the interplay between dark matter and modified gravity. This work examines black holes immersed in perfect fluid dark matter (PFDM) within the Kalb–Ramond (KR) gravity framework. The KR field, a rank-2 antisymmetric tensor, introduces additional degrees of freedom that alter spacetime geometry and affect particle dynamics. We derive the metric for a black hole embedded in PFDM and analyze the circular motion of test particles. By investigating the effective potential, energy, and angular momentum, we determine conditions for stable circular orbits and explore the impact of KR field parameters and PFDM properties. Beyond kinematics, we study quasi-periodic oscillations (QPOs) commonly observed in the X-ray spectra of black hole accretion disks. We link QPO frequencies to orbital properties in our model, proposing an observational test to distinguish KR gravity with PFDM from general relativity. Additionally, we explore the thermodynamic aspects of these black holes, calculating temperature, entropy, and heat capacity to assess the impact of the KR field and PFDM on stability and phase transitions. Radiation properties are also investigated, including modifications to radiation due to the influence of the PFDM and the KR field on the event horizon. Our results reveal that KR gravity and PFDM generate distinctive signatures in particle dynamics, QPO patterns, thermodynamics, and radiation, offering potential observational tests to differentiate these models from standard general relativity (GR).

We investigate the dynamics of charged black holes within the framework of Verlinde's emergent gravity, focusing on their implications for circular orbits and quasiperiodic oscillations (QPOs). Verlinde’s theory modifies the traditional picture of gravitation by introducing entropy-based corrections, interpreted as effects from apparent dark matter. In this context, we construct regular black hole solutions characterized by nonsingular spacetime geometries and analyze how these modifications affect geodesic motion. We derive the effective potential for neutral test particles, identify conditions for circular stability, and compute the innermost stable circular orbit (ISCO). The fundamental frequencies associated with geodesic motion—Keplerian, radial, and vertical epicyclic frequencies—are calculated and compared across different parameter regimes. We further examine how these frequencies translate into observable quasiperiodic oscillations by applying resonance models to fit the twin-peak QPO data from the microquasar GRS 1915+105. The study reveals that the entropy-induced corrections in Verlinde gravity significantly influence the ISCO radius and frequency structure. Our results suggest that timing signals in X-ray binaries offer promising observational tests for modified gravity models like Verlinde's.