Exact solutions of the Dirac equation in spherical Rindler coordinates reveal quantum behaviors near black holes, indicating novel applications in theoretical physics.
The exact solution to the Dirac equation corresponding to a bound state in the spherical Rindler metric is derived and its relation to the near-horizon Schwarzschild metric is investigated. It is shown how to represent these solutions with a specially chirped free-electron wave packet. The spherical Rindler frame stands out as being invariant under Lorentz transformations, in contrast with the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>1</a:mn><a:mo>+</a:mo><a:mn>1</a:mn><a:mi mathvariant="normal">D</a:mi></a:mrow></a:math> Rindler coordinates, and has been used in the description of the so-called spacetime. With heuristic modification of the wave function of the chirped free-electron wave packet quantitative predictions for the quantum properties of the electron crossing the black hole horizon are obtained.
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Campos et al. (2025) studied this question.
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