Tunnelling across a trapped region and out of a black hole

TL;DR

This paper investigates quantum tunnelling of particles across a non-singular black hole's horizons, revealing a non-zero probability of escape influenced by the spacetime's surface gravity, with implications for black hole physics.

Contribution

It demonstrates a non-zero tunnelling probability in a two-dimensional black hole model, dependent on horizon surface gravities, extending understanding of quantum effects near black holes.

Findings

Tunnelling probability asymptotes to a maximum value based on horizon surface gravities.

Transition amplitude between states inside the inner horizon and outside the outer horizon is non-zero.

Tunnelling probability is polynomially suppressed by the inverse surface gravities sum.

Abstract

The quantum field theory for a massless scalar field on a two-dimensional non-singular black hole spacetime gives a non-vanishing probability for a particle to tunnel out of the black hole. The black hole spacetime contains an outer and an inner horizon, and the transition amplitude between a one-particle state localized inside the inner horizon, and a one-particle state localized outside the outer horizon is non-zero, even when the regions where the states are localized are causally disconnected. The total tunnelling probability asymptotes to a maximal value that depends on the background spacetime geometry only through the surface gravity of the two horizons, and is polynomially suppressed by the sum of the inverse surface gravities of the inner and outer horizons.