On the quantization of the extremal Reissner-Nordstrom black hole

Abstract

Following Rosen's quantization rules, two of the Authors (CC and FF) recently described the Schwarzschild black hole (BH) formed after the gravitational collapse of a pressureless "star of dust" in terms of a "gravitational hydrogen atom". Here we generalize this approach to the gravitational collapse of a charged object, namely, to the geometry of a Reissner-Nordstrom BH (RNBH) and calculate the gravitational potential, the Schrödinger equation and the exact solutions of the energy levels of the gravitational collapse. By using the concept of BH effective state, previously introduced by one of us (CC), we describe the quantum gravitational potential, the mass spectrum and the energy spectrum for the extremal RNBH. The area spectrum derived from the mass spectrum finds agreement with a previous result by Bekenstein. The stability of these solutions, described with the Majorana approach to the Archaic Universe scenario, show the existence of oscillatory regimes or exponential damping for the evolution of a small perturbation from a stable state.

arXiv comment7 pages, to appear in Europhysics Letters

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Cited by in corpus (6)

• Schrödinger and Klein-Gordon theories of black holes from the quantization of the Oppenheimer and Snyder gravitational collapse
• Quantum Thermodynamics of an ${\alpha }^{\prime }$-Corrected Reissner-Nordström Black Hole
• Quantum oscillations in the black hole horizon
• "Time"-covariant Schrödinger equation and the canonical quantization of the Reissner-Nordström black hole
• Black hole spectra from Vaz's quantum gravitational collapse
• Time-covariant Schrödinger equation and invariant decay probability: The $\Lambda$-Kantowski-Sachs universe