Hawking radiation as quantum mechanical reflection. (English) Zbl 1515.83058
Summary: In this article, we explore an alternative derivation of Hawking radiation. Instead of the field-theoretic derivation, we have suggested a simpler calculation based on quantum mechanical reflection from a one-dimensional potential. The reflection coefficient shows an exponential fall in energy which, in comparison with the Boltzmann probability distribution, yields a temperature. The temperature is the same as Hawking temperature for spherically symmetric black holes. The derivation gives an exact local calculation of Hawking temperature that involves a region lying entirely outside the horizon. This is a crucial difference from the tunneling calculation, where it is necessary to involve a region inside the horizon.
MSC:
| 83C30 | Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory |
| 83C57 | Black holes |
| 83C45 | Quantization of the gravitational field |
| 51F15 | Reflection groups, reflection geometries |
| 76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |
| 80A10 | Classical and relativistic thermodynamics |
| 52A55 | Spherical and hyperbolic convexity |
| 81U26 | Tunneling in quantum theory |
Software:
DLMFReferences:
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