Tunnelling Methods and Hawking's radiation: achievements and prospects

Understand

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.