Causal structure and optical signatures of rotating power law Kalb-Ramond geometry

Abstract: We investigate a stationary and axisymmetric power law Kalb-Ramond geometry, obtained as a rotating extension of the asymptotically flat static solution. We reconstruct the exact inverse Einstein source supporting the geometry and determine its energy conditions and curvature properties. We characterize the horizon and stationary limit configurations and quantify the outer ergoregion through its angular dependent radial thickness plus its coordinate and proper spatial volumes. We derive the unstable spherical photon region and show that the Kalb-Ramond deformation shifts the prograde photon orbit into the ergoregion at lower spin, while the retrograde region remains outside throughout the entire domain. From the unstable photon region, we construct the exact vacuum critical curve and analyze its area equivalent diameter and displacement, including comparisons with M87$<sup>\ast$ and Sgr~A$<sup>\ast$ within the asymptotically admissible domain. We further examine the fixed-$J$ geometric behavior and rotational energy extraction, with emphasis to rotating weak deflection and two dimensional weak lensing, commenting the physical consequences of our solution in terms of observable outcomes.