Tunneling method for Hawking radiation in the Nariai case

TL;DR

This paper investigates Hawking radiation in the charged Nariai spacetime using tunneling methods and exact solutions, providing a detailed analysis of particle creation near multiple horizons.

Contribution

It offers a comprehensive comparison of tunneling and exact solution approaches to Hawking radiation in the Nariai case, enhancing understanding of quantum effects in complex black hole geometries.

Findings

Confirmation of the tunneling interpretation of Hawking radiation.

Derivation of particle flux using exact solutions of Klein-Gordon equations.

Validation of semiclassical results through S-matrix analysis.

Abstract

We revisit the tunneling picture for the Hawking effect in light of the charged Nariai manifold, because this general relativistic solution, which displays two horizons, provides the bonus to allow the knowledge of exact solutions of the field equations. We first perform a revisitation of the tunneling ansatz in the framework of particle creation in external fields a la Nikishov, which corroborates the interpretation of the semiclassical emission rate Gamma as the conditional probability rate for the creation of a couple of particles from the vacuum. Then, particle creation associated with the Hawking effect on the Nariai manifold is calculated in two ways. On the one hand, we apply the Hamilton Jacobi formalism for tunneling, in the case of a charged scalar field on the given background. On the other hand, the knowledge of the exact solutions for the Klein Gordon equations on Nariai manifold, and their analytic properties on the extended manifold, allow us a direct computation of the flux of particles leaving the horizon, and, as a consequence, we obtain a further corroboration of the semiclassical tunneling picture from the side of S-matrix formalism.