Calculation of Hawking Radiation in Local Field Theory

TL;DR

This paper calculates Hawking radiation and entanglement entropy of blackholes within local field theory, showing radiation is unitary and entropy is a universal constant linked to the horizon area and Hawking radiation.

Contribution

It introduces a local field theory approach to Hawking radiation, demonstrating unitarity and deriving a universal entanglement entropy independent of blackhole parameters.

Findings

Hawking radiation is a unitary process with no information loss.

Entanglement entropy is a universal constant, independent of blackhole parameters.

The entanglement entropy relates to Hawking radiation and horizon area through specific formulas.

Abstract

Hawking radiation of the blackhole is calculated based on the principle of local field theory. In our approach, the radiation is a unitary process, therefore no information loss will be recorded. In fact, observers in different regions of the space communicate using the Hawking radiation, when the systems in the different regions are entangled with each other. The entanglement entropy of the blackhole is also calculated in the local field theory. We found that the entanglement entropy of the systems separated by the blackhole horizon is closely connected to the Hawking radiation in our approach. Our calculation shows that the entanglement entropy of the systems separated by the horizon of a blackhole is just a pure number $\frac{\pi^3 + 270 \zeta(3)}{360 \pi^2}$, independent of any parameter of the blackhole, and its relation to the Hawking radiation is given by $S_{EE} = \frac{8 \pi}{3} \frac{\pi^3 + 270 \zeta(3)}{\pi^3 + 240 \zeta(3)} {\cal A} R_H$, where $S_{EE}$ is the entanglement entropy, $\cal A$ is the area of the horizon, and $R_H$ is the Hawking radiation.