Stationary world lines and the vacuum excitation of noninertial detectors

The stationary world lines, on which quantized field detectors in a vacuum have time-independent excitation spectra, are discussed. They are characterized by the requirement that the geodetic interval between two points depends only on the proper time interval. To construct these world lines a generalization of the Frenet equations to Minkowski space is developed. The curvature invariants are found to be the proper acceleration and angular velocity of the world line. The equations are solved for constant invariants and the solutions are shown to be the stationary world lines. A classification into six types is made. The equivalence of the timelike Killing vector field orbits and the stationary world lines is demonstrated. The classification scheme therefore extends to Killing orbits and stationary coordinate systems in flat spacetime. Finally, the vacuum excitation spectra of detectors on a representative sample of the stationary world lines are calculated.