Blandford-Znajek Scaling in a Power-Law Rotating Kalb-Ramond Geometry: Magnetic-Flux Systematics and Bayesian Identifiability
Relativistic jets from spinning black holes offer a possible strong-field probe of gravity through the Blandford-Znajek mechanism. We study the leading jet-power scaling in the four-dimensional power-law rotating Kalb-Ramond geometry introduced by Kumar, Ghosh, and Wang. The metric is used here as a stationary background, without assuming that it constitutes a newly established exact rotating solution. We first examine the deformation at the metric level. For $s=2$ it is absorbed completely by a mass redefinition, whereas for $s>2$ the correction decays more slowly than the usual mass term. Our main benchmark is therefore the nondegenerate $s=3/2$ case, whose correction falls faster than the Kerr mass term; $s=3$ is kept as a secondary comparison. We evaluate the BZ scaling under three magnetic assumptions: fixed total horizon flux, fixed local normal field with the proper horizon area, and a reduced radius-based flux proxy. The resulting trends differ appreciably, showing that the magnetic prescription is itself a leading systematic. For GRO J1655-40 and GRS 1915+105, the marginalized deformation posterior remains close to the horizon-conditioned effective prior for both a uniform prior and a truncated-Gaussian alternative. The jet-only profile likelihood is also nearly flat over the allowed deformation range, with the same qualitative behavior in the $s=3$ test. Thus, within the present setup, the jet-power proxies do not independently determine the Kalb-Ramond deformation. A stronger inference will require better control of the rotating background, source-dependent magnetic flux, non-Kerr spin estimates, and a larger sample.