Model dependent analytic spin torsion corrections to Blandford Znajek energy extraction in Einstein Cartan gravity

Abstract: We investigate the leading near-horizon response of Blandford-Znajek energy extraction to a compact, neutral spin-polarized source within minimally coupled Einstein-Cartan-Dirac-Maxwell theory. Eliminating the algebraic contortion yields an effective axial contact interaction, which we embed into a conserved, anisotropic phenomenological completion. Working at leading order in the torsion parameter $ε<em>T$, spatial anisotropy $ξ$, and slow rotation $χ=a/M$ on the fixed-ADM branch, we derive the modified energy extraction rate at optimal load. We find that the leading-order power ratio $$P</em>{\rm BZ}^{\rm EC}/P_{\rm BZ}^{\rm K}$$ receives distinct contributions from rotational dragging ($\ell=1$) and magnetostatic flux redistribution ($\ell=2$). In the isotropic limit ($ξ=0$), the power is enhanced for a co-rotating completion and suppressed for a counter-rotating one, whereas for $ξ\neq0$ the net shift depends on the polar quadrupole response. We also formulate the generalized Znajek identity and linearized Grad--Shafranov framework, demonstrating that undetermined load-factor shifts leave the leading power coefficient invariant due to stationarity at the matched load point.