Exact solution of the Dirac equation in spherical Rindler coordinates

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.