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

PABLO ALEJANDRO SÁNCHEZ; JESÚS MARTÍN ROMERO; MAURICIO BELLINI

EUROPEAN PHYSICAL JOURNAL C - PARTICLES AND FIELDS

SPRINGER

Lugar: Berlin; Año: 2011 vol. 71 p. 1526 - 1535

1434-6044

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 TH: E(?ª?«) n = −2?Î i nTH. Furthermore, as one expects for SUSY Hamiltonians, the isolated bottom state has a real null energy eingenvalue.