Tunneling method for Hawking radiation in the Nariai case

Understand

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.