# Moving Mirrors, Black Holes, Hawking Radiation and All That

## Abstract

In this talk I show how, in Lemaitre coordinates, one can canonically quantize a massless scalar field in the background of a Schwarzschild black hole and then show how this leads to a simplified derivation of Hawking radiation. The key result of the canonical quantization procedure is that the Hamiltonian of the system is explicitly time dependent, which immediately shows that the problem is intrinsically non-static and that, although a unitary time-development operator exists, it is not useful to talk about eigenstates. Rather, one should deal with the Heisenberg equations of motion and focus attention on steady state phenomena, such as the Hawking radiation. In order to clarify the procedure used to solve the Heisenberg equations I first discuss the related problem of the massless scalar field theory calculated in the presence of a moving mirror.

- Authors:

- Publication Date:

- Research Org.:
- Stanford Linear Accelerator Center, Menlo Park, CA (US)

- Sponsoring Org.:
- USDOE Office of Energy Research (ER) (US)

- OSTI Identifier:
- 798918

- Report Number(s):
- SLAC-PUB-9047

TRN: US200222%%117

- DOE Contract Number:
- AC03-76SF00515

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 8 Nov 2001

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BLACK HOLES; EIGENSTATES; EQUATIONS OF MOTION; HAMILTONIANS; MIRRORS; QUANTIZATION; RADIATIONS; SCALAR FIELDS

### Citation Formats

```
Weinstein, Marvin.
```*Moving Mirrors, Black Holes, Hawking Radiation and All That*. United States: N. p., 2001.
Web. doi:10.2172/798918.

```
Weinstein, Marvin.
```*Moving Mirrors, Black Holes, Hawking Radiation and All That*. United States. https://doi.org/10.2172/798918

```
Weinstein, Marvin. Thu .
"Moving Mirrors, Black Holes, Hawking Radiation and All That". United States. https://doi.org/10.2172/798918. https://www.osti.gov/servlets/purl/798918.
```

```
@article{osti_798918,
```

title = {Moving Mirrors, Black Holes, Hawking Radiation and All That},

author = {Weinstein, Marvin},

abstractNote = {In this talk I show how, in Lemaitre coordinates, one can canonically quantize a massless scalar field in the background of a Schwarzschild black hole and then show how this leads to a simplified derivation of Hawking radiation. The key result of the canonical quantization procedure is that the Hamiltonian of the system is explicitly time dependent, which immediately shows that the problem is intrinsically non-static and that, although a unitary time-development operator exists, it is not useful to talk about eigenstates. Rather, one should deal with the Heisenberg equations of motion and focus attention on steady state phenomena, such as the Hawking radiation. In order to clarify the procedure used to solve the Heisenberg equations I first discuss the related problem of the massless scalar field theory calculated in the presence of a moving mirror.},

doi = {10.2172/798918},

url = {https://www.osti.gov/biblio/798918},
journal = {},

number = ,

volume = ,

place = {United States},

year = {2001},

month = {11}

}