Quantum instability for charged scalar particles on charged Nariai and ultracold black hole manifolds

TL;DR

This paper investigates quantum instabilities of charged scalar fields in specific charged black hole backgrounds, calculating the effective action's imaginary part and considering thermal effects, thus advancing understanding of quantum effects in curved spacetime.

Contribution

It provides exact calculations of quantum instability measures for charged scalar fields on ultracold and Nariai black hole backgrounds, including thermal effects, using multiple analytical methods.

Findings

Computed the imaginary part of the effective action exactly.

Analyzed quantum instability in various charged black hole backgrounds.

Included thermal effects in the stability analysis.

Abstract

We analyze in detail the quantum instability which characterizes charged scalar field on three special de Sitter charged black hole backgrounds. In particular, we compute exactly the imaginary part of the effective action for scalar charged fields on the ultracold I, ultracold II and Nariai charged black hole backgrounds. Both the transmission coefficient approach and the $\zeta$-function approach are exploited. Thermal effects on this quantum instability are also taken into account in presence of a non-zero black hole temperature (ultracold I and Nariai).