Quantum mechanical path integrals and thermal radiation in static curved spacetimes

TL;DR

This paper uses quantum mechanical path integrals to analyze the propagator and thermal radiation in static curved spacetimes with horizons, demonstrating the role of topology and complex coordinates in these phenomena.

Contribution

It introduces a novel path integral approach to static curved spacetimes with horizons, emphasizing topology and complex tortoise coordinates for thermal behavior analysis.

Findings

Propagator exhibits thermal properties linked to topology.

Quantum evolution across horizons remains unitary.

Complex tortoise coordinates unify spacetime regions.

Abstract

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.