Quantum Fields in Schwarzschild-de Sitter Space

TL;DR

This paper explores quantum fields in Schwarzschild-de Sitter space within the No-Boundary Universe, analyzing black hole creation, thermal states, and the purity of the no-boundary state in specific models.

Contribution

It introduces a new internal parameter in the constrained gravitational instanton and examines its effect on the thermal properties of quantum fields in this spacetime.

Findings

Perturbation modes are in thermal equilibrium at arbitrary temperatures.

The no-boundary state remains pure in de Sitter and Nariai models.

The internal parameter influences the temperature of the perturbation modes.

Abstract

In the No-Boundary Universe a primordial black hole is created from a constrained gravitational instanton. The black hole created is immersed in the de Sitter background with a positive cosmological constant. The constrained instanton is characterized not only by the external parameters, the mass parameter, charge and angular momentum, but also by one more internal parameter, the identification period in the imaginary time coordinate. Although the period has no effect on the black hole background, its inverse is the temperature of the no-boundary state of the perturbation modes perceived by an observer. By using the Bogoliubov transformation, we show that the perturbation modes of both scalar and spinor fields are in thermal q equilibrium with the black hole background at the arbitrary temperature. However, for the two extreme cases, the de Sitter and the Nariai models, the no-boundary state remains pure.