Schrödinger equation in a general curved spacetime geometry

We consider relativistic quantum field theory in the presence of an external electric potential a general curved space-time geometry. utilise Fermi coordinates adapted to time-like geodesic describe low-energy physics laboratory and calculate leading correction due curvature geometry Schr\"odinger equation. then compute non-vanishing probability excitation for hydrogen atom that falls or is scattered by Schwarzschild black hole. The photon emitted from excited state spontaneous emission extracts energy hole, increases decay rate hole adds information paradox.