Energy extraction and Keplerian fundamental frequencies in the Kalb–Ramond gravity

The nonminimal coupling of the nonzero vacuum expectation value of the self-interacting antisymmetric Kalb–Ramond field with gravity leads to a power-law hairy BH having a parameter $s$, which encompasses the Reissner-Nordström black hole ($s=1$). It is obtained the axially symmetric counterpart of this hairy solution, namely, the rotating Kalb–Ramond black hole, which encompasses, as special cases, Kerr ($s=0$) and Kerr–Newman ($s=1$) black holes. With rotating Kalb–Ramond black hole metric, we study its horizon structure and motion of the test particles in the near of the equatorial plane and we determine radial motion equations which governing $t$ and $\varphi$. We also explore thatthe black hole mass increasing when falling many of mass-less particles are relative to the black hole mass. We consider how the Kalb–Ramond parameters depend on increasing its mass. Furthermore, we analyze the Keplerian frequency, as well as the vertical and horizontal oscillations of basic frequencies, using a graph-based approach. The frequency charts are contingent upon the Kalb–Ramond parameters $s$ and $\Gamma$. By consulting certain sources, ones can investigate the distinctions between KR gravity and other models.