Examining a covariant and renormalizable quantum field theory in de Sitter space by studying "black hole radiation"

TL;DR

This paper demonstrates that the Krein-Gupta-Bleuler formalism in de Sitter space naturally produces Hawking radiation, providing a covariant, renormalized quantum field theory framework that aligns with black hole thermodynamics.

Contribution

It introduces a covariant, renormalized quantization scheme in de Sitter space that inherently accounts for black hole radiation without pathological behavior.

Findings

The formalism yields a vanishing vacuum energy due to automatic renormalization.

It shows black holes produce Hawking radiation with temperature matching standard results.

The approach avoids large-distance pathologies in quantum field theory on curved backgrounds.

Abstract

Respecting that any consistent quantum field theory in curved space-time must include black hole radiation, in this paper, we examine the Krein-Gupta-Bleuler (KGB) formalism as an inevitable quantization scheme in order to follow the guideline of the covariance of minimally coupled massless scalar field and linear gravity on de Sitter (dS) background in the sense of Wightman-G\"{a}rding approach, by investigating thermodynamical aspects of black holes. The formalism is interestingly free of pathological large distance behavior. In this construction, also, no infinite term appears in the calculation of expectation values of the energy-momentum tensor (we have an automatic and covariant renormalization) which results in the vacuum energy of the free field vanishes. However, the existence of an effective potential barrier, intrinsically created by black holes gravitational field, gives a Casimir-type contribution to the vacuum expectation value of the energy-momentum tensor. On this basis, by evaluating the Casimir energy-momentum tensor for a conformally coupled massless scalar field in the vicinity of a non-rotating black hole event horizon through the KGB quantization, in this work, we explicitly prove that the hole produces black-body radiation which its temperature exactly coincides with the result obtained by Hawking for black hole radiation.