One-electron atom in curved space-time

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Astrophysics, Atomic Energy Levels, Relativistic Effects, Space-Time Functions, Atomic Spectra, Curvature, Dirac Equation, Hamiltonian Functions

Scientific paper

Consideration is given to shifts in the energy levels of a one-electron atom induced by a general curved space-time, which shifts would allow the determination of space-time curvature from atomic spectra. The Hamiltonian of the Dirac equation is obtained in Fermi normal coordinates, and expressions are derived to first order in the Riemann tensor for the energy shifts the 1S(1/2), 2S(1/2) and 2P(1/2) levels. It is pointed out that the space-time curvature affects each energy level to a different degree, in contrast to the uniform effects of the Doppler, gravitational and cosmological shifts.

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