On the Hawking radiation as tunneling for a class of dynamical black holes

The instability against emission of massless particles by the trapping horizon of an evolving black hole is analyzed with the use of the Hamilton-Jacobi method. The method automatically selects one special expression for the surface gravity of a changing horizon. Indeed, the strength of the horizon singularity turns out to be governed by the surface gravity as was defined a decade ago by Hayward using Kodama's theory of spherically symmetric gravitational fields. The theory also applies to point masses embedded in an expanding universe, were the surface gravity is still related to Kodama-Hayward theory. As a bonus of the tunneling method, we gain the insight that the surface gravity still defines a temperature parameter as long as the evolution is sufficiently slow that the black hole pass through a sequence of quasi-equilibrium states.Comment: added references for section 1, corrected typos, some improvement in notatio

Fermions Tunnelling from Black Holes

We investigate the tunnelling of spin 1/2 particles through event horizons. We first apply the tunnelling method to Rindler spacetime and obtain the Unruh temperature. We then apply fermion tunnelling to a general non-rotating black hole metric and show that the Hawking temperature is recovered.Comment: 22 pages, v2: added references, v3: fixed minor typos, v4: added a new section applying fermion tunnelling method to Kruskal-Szekers coordinates, fixed minor typo, and added references, v5: modified introduction and conclusion, fixed typo