Hawking Radiation via Complex Geodesics

TL;DR

This paper models Hawking radiation as quantum tunneling of massive particles from Kerr black holes using complex geodesic trajectories, leading to a derivation of the thermal spectrum.

Contribution

It introduces a detailed worldline approach with complex trajectories to analyze particle tunneling in Kerr black holes, connecting Hamiltonian dynamics with quantum radiation.

Findings

Trajectories are smooth and cover horizon regions.

Density of states is linear in momenta at leading order.

Thermal spectrum proportional to the fourth power of Hawking temperature.

Abstract

We describe in detail the quantum tunneling of massive particles from Kerr black hole by using complex trajectories, which are solutions to the Hamilton's equations of motion with imaginary proper time. The trajectories are smooth and cover the inner and outer horizon regions. Following the worldline approach, we compute the energy flux at the event horizon as a summation over these complex trajectories. Density of states is given with the aid of Carter's constant and it is shown to be linear in momenta in the leading order, as long as the phase portrait of the system stays uniform. Under this assumption, we obtain the thermal spectrum $\sim (T^{+}_H)^4$.