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We use the Fock-Ivanenko formalism to obtain the Dirac equation whichdescribes the interaction of a massless 1/2-spin neutral fermion with agravitational field around a Schwarzschild black hole (BH). We obtainapproximated analytical solutions for the eigenvalues of the energy(quasi-normal frequencies) and their corresponding eigenstates (quasi-normalstates). The interesting result is that all the excited states [and theirsupersymmetric (SUSY) partners] have a purely imaginary frequency, which can beexpressed in terms of the Hawking temperature. Furthermore, as one expects forSUSY Hamiltonians, the isolated bottom state has a real null energy eigenvalue.

Analytical treatment of SUSY Quasi-normal modes in a non-rotating Schwarzschild black hole