The connection between Unruh scheme and Damour-Ruffini scheme in rindler space-time and η-ε space-time

Abstract

It is shown in the Rindler space-time and the η-ε space-time that there exists an intrinsic connection between the Unruh’s scheme and the Damour-Ruffini’s scheme dealing with the Hawking-Unruh effect. The analytic functions by Unruh to construct the Fock space can come from the analytic continuation of the Damour-Ruffini type. Both the Bogoliubov transformation method by Unruh and the analytic continuation method by Damour-Ruffini come to the same result. A pure ground-state analytic wave function defined on a connected complex manifold is a mixed thermal state on its real Lorentzian section separated into several regions, no matter what the boundaries of the regions may be, event horizons or infinite points.