On tunneling across horizons

TL;DR

This paper defends and refines the tunneling method for black hole radiation, demonstrating its consistency, covariance, and extensions to spinning particles, based on analytic continuation of the classical action.

Contribution

It shows that the tunneling method can be made consistent and covariant, extending it to spinning particles and simplifying its application through analytic continuation.

Findings

Tunneling trajectories are correctly identified, removing inconsistencies.

The method is manifestly covariant and extendable to spinning particles.

A simpler analytic continuation approach supports the tunneling framework.

Abstract

The tunneling method for stationary black holes in the Hamilton-Jacobi variant is reconsidered in the light of various critiques that have been moved against. It is shown that once the tunneling trajectories have been correctly identified the method isfree from internal inconsistencies, it is manifestly covariant, it allows for the extension to spinning particles and it can even be used without solving the Hamilton-Jacobi equation. These conclusions borrow support on a simple analytic continuation of the classical action of a pointlike particle, made possible by the unique assumption that it should be analytic in complexified Schwarzschild or Kerr-Newman spacetimes. A more general version of the Parikh-Wilczek method will also be proposed along these lines.