Hawking Radiation as Tunneling

TL;DR

The paper reformulates Hawking radiation as a semi-classical tunneling process in a dynamical spacetime, enforcing energy conservation via back-reaction. By computing the imaginary part of the action for horizon-crossing emission and showing the rate equals $\Gamma \sim e^{\Delta S_{\rm B-H}}$, it derives a non-thermal spectrum with higher-order corrections in the emitted energy $\omega$. The method, which generalizes to charged black holes, contrasts with traditional fixed-background treatments and highlights horizon dynamics and local contour prescriptions as central to the time asymmetry of radiation. The non-thermal corrections suggest potential information-carrying correlations in the radiation, offering a conceptually transparent link between tunneling and black hole thermodynamics.

Abstract

We present a short and direct derivation of Hawking radiation as a tunneling process, based on particles in a dynamical geometry. The imaginary part of the action for the classically forbidden process is related to the Boltzmann factor for emission at the Hawking temperature. Because the derivation respects conservation laws, the exact spectrum is not precisely thermal. We compare and contrast the problem of spontaneous emission of charged particles from a charged conductor.