Planckian charged black holes and their cosmological ramifications

TL;DR

This paper introduces a regularized model of Planck-scale charged black holes using nonlinear electrodynamics, exploring their thermodynamics, cosmological implications, and quantum pair creation in anti-de Sitter and de Sitter spaces.

Contribution

It develops a novel regularized charged black hole solution incorporating minimal length effects and analyzes its thermodynamics and quantum cosmological production.

Findings

Black holes are free from ultraviolet divergences.

Thermodynamics shows Van der Waals-like behavior.

Black hole pair creation rates are computed in cosmological backgrounds.

Abstract

The application of nonlinear electrodynamics at high energy scales has led to a variety of interesting phenomena in recent years, particularly within the context of non-singular spacetime geometries. Additionally, it is postulated that gravity near the Planck scale is governed by a minimal cut-off length, which acts as a renormalization scale against ultraviolet pathologies. Within this framework, we combine both concepts by introducing modifications to the electric and matter sectors of a black hole as its size approaches this minimal length. The result is an electrically charged black hole that is free from ultraviolet divergences and recovers the Maxwell limit at classical scales. We further explore the geometric and thermodynamic properties of the resulting solution within a cosmological anti-de Sitter background, revealing a chemical analogy with that of a Van der Waals fluid. Subsequently, we examine the charged black hole in de Sitter space and construct four corresponding gravitational instantons. We then study their cosmological quantum production using the formalism of the pair creation rate within the context of the no-boundary proposal.