Eur. Phys. J. C 71, 1526 (2011)
https://doi.org/10.1140/epjc/s10052-010-1526-9

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

¹ Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, 7600, Mar del Plata, Argentina
² Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata, Argentina

mbellini@mdp.edu.ar

Received: 14 October 2010
Revised: 15 November 2010
Published online: 13 January 2011

Abstract

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