Quantum Instability for Charged Particles on Charged Nariai Black Hole Manifold: Exact 4D Results for Black Hole Discharge Phenomenon

摘要

Spontaneous loss of charge by a charged black hole is a relevant topic in the framework of quantum effects in the field of a black hole. It belongs to the framework of phenomena which are due to vacuum instability in presence of an external field, with consequent pair creation. Quantum-electrodynamics effects in presence of an external electric field have been in particular a key-topic which has been extensively discussed. In black hole manifolds, discharge process has been considered at first in the case of Reissner-Nordstr?m black holes. Still, analytical results are limited to the semiclassical approximation (WKB). We first review some aspects of the theory of pair creation in presence of an external electrostatic field, as discussed in the seminal paper by J.Schwinger, and its relation with the so-called Klein paradox. Furthermore, we recall some basic aspects of pair creation in charged black hole backgrounds, with particular reference to the Damour-Deruelle-Ruffini method. Then we provide an example of exact calculations for the quantum instability which is at the root of the spontaneous discharge process for 4D charged black holes, by exploiting the property of the charged Nariai black hole background to allow to bring back the problem to a Kaluza-Klein reduction. Both the zeta-function approach and the transmission coefficient approach are taken into account in order to calculate the imaginary part of the effective action, which signals the presence of an instability phenomenon for the quantum vacuum. A comparison between the two methods is also provided, as well as a comparison with WKB results. Finally, we also take into account how thermal effects, which are associated with the presence of a non-zero black hole temperature, affect the discharge process.