Tunnelling Methods and Hawking's radiation: achievements and prospects

TL;DR

This paper reviews the tunnelling method as an alternative way to understand Hawking radiation, discussing its formulation, equivalence of main approaches, and extensions to dynamic horizons, highlighting achievements and future prospects.

Contribution

It provides a comprehensive review of tunnelling methods for Hawking radiation, including their formulation, equivalence, and extensions to dynamic black holes and horizons.

Findings

Null geodesic and Hamilton-Jacobi methods are equivalent for stationary black holes.

The Hamilton-Jacobi method is extended to dynamical black holes and cosmological horizons.

Prospects and achievements of tunnelling approaches are discussed.

Abstract

The aim of this work is to review the tunnelling method as an alternative description of the quantum radiation from black holes and cosmological horizons. The method is first formulated and discussed for the case of stationary black holes, then a foundation is provided in terms of analytic continuation throughout complex space-time. The two principal implementations of the tunnelling approach, which are the null geodesic method and the Hamilton-Jacobi method, are shown to be equivalent in the stationary case. The Hamilton-Jacobi method is then extended to cover spherically symmetric dynamical black holes, cosmological horizons and naked singularities. Prospects and achievements are discussed in the conclusions.