Massive neutral Dirac quasibound states in a Newman-Janis-generated rotating charged Kalb-Ramond black-hole geometry

Abstract

We study quasibound states of a massive neutral Dirac field in the Newman-Janis-generated rotating charged geometry used in Lorentz-violating Kalb-Ramond (KR) gravity. Rather than assuming that the Kerr separation survives the deformation, we first recast the metric in four-dimensional off-shell Carter form. The corresponding principal closed conformal Killing-Yano tensor then provides the hidden symmetry needed to separate the torsion-free, minimally coupled Dirac equation. We derive the horizon and large-radius boundary conditions, including the non-Minkowskian asymptotic normalization, and determine the complex spectrum from coupled angular and matrix radial continued fractions. The code reproduces the Kerr spectrum and is checked by truncation studies and independent two-sided radial integrations. In scans at fixed metric parameters, increasing the KR parameter moves most real frequencies toward the mass threshold and reduces most decay rates. These trends are not invariant, however, because the same variation changes both the asymptotic potential scale and the distance from extremality. A scan in which these two quantities are held fixed changes the absolute ground-state trend but preserves a reversal in the real-frequency ordering of the maximal-$m$, $j=3/2$, $\ell=1$ pair. The location of the crossing shifts with the normalization convention. Thus the level reordering is more robust than the individual monotonic trends in binding energy or lifetime within this background family.