Exotic Spinor Deformation of a Schwarzschild Black Hole: Perturbations and Stability

Abstract

In this work we investigate how exotic spinorial topology modifies the propagation of fermionic modes in the Schwarzschild geometry. By incorporating a topological gradient, $\partial_μφ$, into the Dirac operator through a tetrad deformation, we show that the exotic spinorial sector naturally induces an effective geometric deformation of the Schwarzschild background. The central consequence of this construction is the emergence of a topological impedance surface at $\rtopo=1/q$, which suppresses the radial group velocity of the exotic spinorial modes, yielding a birefringent propagation pattern. Using a spinorial perturbation we discuss the greybody factor and the quasinormal response. The quasinormal spectrum shows the stability of the background metric and the absence of isospectrality for the superpartner potentials.