Hey all! I'm new to Physics Forums. I'm going through Hawking's famous 1975 paper "Particle Creation by Black Holes" which presents the phenomenon later known as Hawking radiation. I'm going through it for the sake of my own learning and benefit since the paper is a bit ahead of my edge as a physics student. And, since I have lots of questions about it, I figured I'd leave them here to see if I can get some answers and share the knowledge.(adsbygoogle = window.adsbygoogle || []).push({});

Q1: Equation 1.1. Yep, the first one. It says if there's a field [itex] \phi [/itex] that satisfies

$$\phi_{; \mu\nu} \eta^{\mu\nu} = 0$$

then one can express [itex] \phi [/itex] as

$$\phi = \sum_i f_i a_i + \bar{f}_i a^\dagger_i$$

where [itex] \eta^{\mu\nu} [/itex] is the Minkowski metric, the [itex] a_i^\dagger ,a_i [/itex] are the usual creation and annihilation operators and [itex] f,\bar{f} [/itex] are the complete, complex, and orthonormal family of solutions to thewave equation[itex] f_{i ; ab} \eta^{ab} = 0[/itex]

I'm leaving out a few subscripts to declutter. Now, here's the questions:

Link to the paper:

- How is [itex] f_{i ; ab} \eta^{ab} = 0[/itex] a wave equation? Can we compare to E&M's [itex] \partial_\mu\partial^\mu A^{\nu} = 0[/itex]?
- Isn't [itex]\phi = \sum_i f_i a_i + \bar{f}_i a^\dagger_i[/itex] something that comes from QM to express a state as a linear expansion of basis states? Why does Hawking put the solution in this form?

- Last, and maybe most important part: why is Hawking considering fields that satisfy [itex]\phi_{\mu\nu} \eta^{\mu\nu} = 0[/itex] in first place?

https://projecteuclid.org/download/pdf_1/euclid.cmp/1103899181

EDIT 3/29: Fixed the things LeandroMdO pointed out.

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# A Paper Spelunking: "Particle Creation by Black Holes" - S.H.

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