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

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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: \(E^{(\uparrow\downarrow)}_{n}=-2\pi i n T_{\mathrm{H}}\). Furthermore, as one expects for SUSY Hamiltonians, the isolated bottom state has a real null energy eigenvalue.

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Authors and Affiliations

  1. Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, 7600, Mar del Plata, Argentina

    Pablo Alejandro Sánchez, Jesús Martín Romero & Mauricio Bellini

  2. Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata, Argentina

    Pablo Alejandro Sánchez, Jesús Martín Romero & Mauricio Bellini

Authors
  1. Pablo Alejandro Sánchez
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  2. Jesús Martín Romero
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  3. Mauricio Bellini
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Correspondence to Mauricio Bellini.

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Sánchez, P.A., Romero, J.M. & Bellini, M. Analytical treatment of SUSY Quasi-normal modes in a non-rotating Schwarzschild black hole. Eur. Phys. J. C 71, 1526 (2011). https://doi.org/10.1140/epjc/s10052-010-1526-9

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  • DOI: https://doi.org/10.1140/epjc/s10052-010-1526-9

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