Calculation of Hawking Radiation in Local Field Theory

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.