Abstract:
In classical general relativity, neither light nor matter can escape from inside the event horizon of a black hole. However, in his 1975 paper, Hawking demonstrated that black holes emit thermal radiation by applying quantum field theory in curved spacetime. This phenomenon is now known as Hawking radiation. In this presentation, we consider a spacetime in which a black hole forms through gravitational collapse and introduce the basic mechanism of Hawking radiation through the quantization of a massless scalar field. In general curved spacetime, the definitions of particles and the vacuum are not necessarily unique. By comparing the mode functions before and after gravitational collapse, we find that positive- and negative-frequency modes become mixed. As a result, a quantum state that is initially defined as the vacuum can be observed as a state containing particles by observers in the distant future. We then explain how this particle creation leads to a thermal factor of the Bose–Einstein distribution, characterized by a temperature inversely proportional to the black hole mass. We also introduce the greybody factor, which describes how scattering by the effective potential outside the black hole modifies the radiation spectrum. Finally, we briefly discuss the decrease in black hole mass due to Hawking radiation, its negative heat capacity, and its relationship to the Bekenstein–Hawking entropy, highlighting the thermodynamic properties of black holes.