The problem of embedded eigenvalues for the Dirac equation in the Schwarzschild black hole metric

Abstract

We use the Dirac equation in a fixed black hole background and different independent techniques to demonstrate the absence of fermionic bound states around a Schwarzschild black hole. In particular, we show that no embedded eigenvalues exist which have been claimed for the case when the energy is less than the particle's mass. We explicitly prove that the claims regarding the embedded eigenvalues can be traced back to an oversimplified approximation in the calculation. We conclude that no bound states exist regardless the value of the mass.

arXiv comment12 pages

References in corpus (7)

• Bound states and decay times of fermions in a Schwarzschild black hole background
• Non-Existence of Time-Periodic Solutions of the Dirac Equation in an Axisymmetric Black Hole Geometry
• On the Eigenvalues of the Chandrasekhar-Page Angular Equation
• The generalized Heun equation in QFT in curved space-times
• The Dirac propagator in the Kerr-Newman metric
• Bound State Solutions of the Dirac Equation in the Extreme Kerr Geometry
• Determining the size of the proton