Superradiant particle production in rotating quantum corrected black hole plasmas

We investigate superradiant particle production in a rotating quantum corrected black hole surrounded by a plasma environment within a controlled phenomenological framework. The spacetime is described by a separable Kerr like effective geometry characterized by the dimensionless spin $$j=a/M$$ j = a / M and quantum correction parameter u=η /η c u = η / η c , while the plasma dressed bosonic mode is represented by a constant effective mass μ ̄eff=Mμ eff μ ¯ eff = M μ eff . We derive the horizon structure, superradiant window, separated field equations, and radial trapping properties. To determine the instability dynamically, we directly solve the complex quasi bound mode problem for the fundamental =m=1 ℓ = m = 1 state, imposing an ingoing boundary condition at the outer horizon and exponential decay at infinity. The numerical implementation is validated in the Kerr limit and tested for convergence. For μ ̄eff=0.15 μ ¯ eff = 0.15 , a positive correction moves the $$j=0.5$$ j = 0.5 configuration through the instability onset at u 0.259 u ≃ 0.259 . For $$j=0.8$$ j = 0.8 , however, the superradiant frequency margin increases while the computed growth rate decreases from 1.54× 10⁻¹⁰ 1.54 × 10 - 10 at $$u=0$$ u = 0 to 9.62× 10⁻¹¹ 9.62 × 10 - 11 at $$u=0.30$$