Quantum mechanical path integrals and thermal radiation in static curved spacetimes

Details Quantum mechanical path integrals and thermal radiation in static curved spacetimes Quantum mechanical path integrals and thermal radiation in static curved spacetimes

1999-06-03

arxiv.org/abs/gr-qc/9906008v1

Phys.Rev. D61 (2000) 044019

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, 10 figures

Scientific paper

10.1103/PhysRevD.61.044019

The propagator of a spinless particle is calculated from the quantum mechanical path integral formalism in static curved spacetimes endowed with event-horizons. A toy model, the Gui spacetime, and the 2D and 4D Schwarzschild black holes are considered. The role of the topology of the coordinates configuration space is emphasised in this framework. To cover entirely the above spacetimes with a single set of coordinates, tortoise coordinates are extended to complex values. It is shown that the homotopic properties of the complex tortoise configuration space imply the thermal behaviour of the propagator in these spacetimes. The propagator is calculated when end points are located in identical or distinct spacetime regions separated by one or several event-horizons. Quantum evolution through the event-horizons is shown to be unitary in the fifth variable.

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