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
Received:
14
October
2010
Revised:
15
November
2010
Published online:
13
January
2011
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.
© Springer-Verlag / Società Italiana di Fisica, 2011