Supersymmetric quasi-normal modes in a non-rotating Schwarzschild black hole

PABLO ALEJANDRO SÁNCHEZ; JESÚS MARTÍN ROMERO; MAURICIO BELLINI

La Plata

Congreso; International School in Quantum Gravity; 2010

We obtain analytical solutions for eigenvalues of energy (quasi-normal fre- quencies) and their corresponding eigenstates (quasi-normal states) in the Dirac equation for a (massless) neutrino that interacts with a gravitational ¯eld driven by a non-rotating neutral Schwarzschild black hole (BH). The interesting result is that all the excited states [and their supersymmetric (SUSY) partners] have a purely imaginary frequency, which can be expressed in terms of the Hawking temperature, once the quantization of quasi-normal modes is obtained. As one expects for SUSY Hamiltonians, the isolated bottom state has a real null-stable-eigenvalue of energy. hat interacts with a gravitationalhat interacts with a gravitational ¯eld driven by a non-rotating neutral Schwarzschild black hole (BH). The interesting result is that all the excited states [and their supersymmetric (SUSY) partners] have a purely imaginary frequency, which can be expressed in terms of the Hawking temperature, once the quantization of quasi-normal modes is obtained. As one expects for SUSY Hamiltonians, the isolated bottom state has a real null-stable-eigenvalue of energy.