Catastrophic Emission of Charges from Near-Extremal Nariai Black Holes

TL;DR

This paper investigates charge emission from near-extremal Nariai black holes, revealing a catastrophic emission process that influences their evolution and stability, using advanced mathematical methods to compare with similar black hole models.

Contribution

It introduces a detailed analysis of charge emission mechanisms in near-extremal Nariai black holes using in-out formalism and monodromy method, highlighting the conditions for catastrophic emission.

Findings

Charge emission becomes catastrophic when charge energy exceeds chemical potential.

Large charge black holes may avoid evolving into naked singularities due to emission effects.

Small charge black holes predominantly emit neutral particles and increase their charge-to-mass ratio.

Abstract

Using both the in-out formalism and the monodromy method, we study the emission of charges from near-extremal charged Nariai black holes with the black hole event and cosmological horizons close to each other, whose near-horizon geometry is $\mathrm{dS}_2 \times \mathrm{S}^2$. The emission becomes catastrophic for a charge with energy greater than its chemical potential, whose leading exponential factor increases inversely proportional to the separation of two horizons. This effect may prevent near-extremal Nariai black holes with large charges that evaporate dominantly through the charge emission from evolving to black holes with a naked singularity, in analog to near-extremal RN-dS black holes that have the Breitenlohner-Friedman bound, below which they become stable against Hawking radiation and Schwinger effect of charge emission. The near-extremal Nariai black holes with small charges, which are close to near-extremal Schwarzschild-dS black holes, emit dominantly charge-neutral particles and evolve to black holes with increasing charge to mass ratio. We illuminate the origin of the catastrophic emission in the phase-integral formulation and monodromy method by comparing near-extremal charged Nariai black holes with near-extremal RN-dS black holes.