Schrödinger equation in a general curved space-time geometry
arXiv:2105.13896 · doi:10.1142/S0218271822500183
Abstract
We consider relativistic quantum field theory in the presence of an external electric potential in a general curved space-time geometry. We utilise Fermi coordinates adapted to the time-like geodesic to describe the low-energy physics in the laboratory and calculate the leading correction due to the curvature of the space-time geometry to the Schrödinger equation. We then compute the non-vanishing probability of excitation for a hydrogen atom that falls in or is scattered by a general Schwarzschild black hole. The photon that is emitted from the excited state by spontaneous emission extracts energy from the black hole, increases the decay rate of the black hole and adds to the information paradox.
39 pages, 9 figures, Matches the published version
References in corpus (12)
- Limits on the Macho Content of the Galactic Halo from the EROS-2 Survey of the Magellanic Clouds
- Cosmic microwave background limits on accreting primordial black holes
- Dark Matter Density Spikes around Primordial Black Holes
- Fermi Coordinates and Penrose Limits
- Do static atoms outside a Schwarzschild black hole spontaneously excite?
- Spontaneous excitation of a static multilevel atom coupled with electromagnetic vacuum fluctuations in Schwarzschild spacetime
- Thermal nature of de Sitter spacetime and spontaneous excitation of atoms
- Imprints from a Riemann-Cartan space-time on the energy levels of Dirac spinors
- Spontaneous excitation of an accelerated atom coupled with quantum fluctuations of spacetime
- Inertial and gravitational effects on a geonium atom
- A Wavefunction Description for a Localized Quantum Particle in Curved Spacetimes
- High frequency background gravitational waves from spontaneous emission of gravitons by hydrogen and helium