# Virtual black holes in a third quantized formalism

## Abstract

In this paper, we will analyse virtual black holes using the third quantization formalism. As the virtual black hole model depends critically on the assumption that the quantum fluctuations dominate the geometry of spacetime at Planck scale, we will analyse the quantum fluctuations for a black hole using third quantization. We will demonstrate that these quantum fluctuations depend on the factor ordering chosen. So, we will show that only certain values of the factor ordering parameter are consistent with virtual black holes model of spacetime foam. - Highlights: • We analyze the Wheeler–DeWitt equation using third quantization. • The quantum fluctuations of geometry is studied using this formalism. • These quantum fluctuations produce virtual black holes. • This model is consistent with only certain values of the factor ordering.

- Authors:

- Division of Mathematical Science, Department of Social Medicine, Faculty of Medicine, University of Miyazaki, Kihara 5200, Kiyotake-cho, Miyazaki, 889-1692 (Japan)
- Department of Physics and Astronomy, University of Lethbridge, Lethbridge, Alberta, T1K 3M4 (Canada)
- (Canada)
- Department of Physics, Ehime university, 2-5 Bunkyo-cho, Matsuyama, 790-8577 (Japan)

- Publication Date:

- OSTI Identifier:
- 22701530

- Resource Type:
- Journal Article

- Journal Name:
- Annals of Physics

- Additional Journal Information:
- Journal Volume: 384; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BLACK HOLES; FIELD OPERATORS; FLUCTUATIONS; QUANTIZATION; QUANTUM FIELD THEORY; SPACE-TIME

### Citation Formats

```
Ohkuwa, Yoshiaki, Faizal, Mir, Irving K. Barber School of Arts and Sciences, University of British Columbia-Okanagan, Kelowna, British Columbia V1V 1V7, and Ezawa, Yasuo.
```*Virtual black holes in a third quantized formalism*. United States: N. p., 2017.
Web. doi:10.1016/J.AOP.2017.06.020.

```
Ohkuwa, Yoshiaki, Faizal, Mir, Irving K. Barber School of Arts and Sciences, University of British Columbia-Okanagan, Kelowna, British Columbia V1V 1V7, & Ezawa, Yasuo.
```*Virtual black holes in a third quantized formalism*. United States. doi:10.1016/J.AOP.2017.06.020.

```
Ohkuwa, Yoshiaki, Faizal, Mir, Irving K. Barber School of Arts and Sciences, University of British Columbia-Okanagan, Kelowna, British Columbia V1V 1V7, and Ezawa, Yasuo. Fri .
"Virtual black holes in a third quantized formalism". United States. doi:10.1016/J.AOP.2017.06.020.
```

```
@article{osti_22701530,
```

title = {Virtual black holes in a third quantized formalism},

author = {Ohkuwa, Yoshiaki and Faizal, Mir and Irving K. Barber School of Arts and Sciences, University of British Columbia-Okanagan, Kelowna, British Columbia V1V 1V7 and Ezawa, Yasuo},

abstractNote = {In this paper, we will analyse virtual black holes using the third quantization formalism. As the virtual black hole model depends critically on the assumption that the quantum fluctuations dominate the geometry of spacetime at Planck scale, we will analyse the quantum fluctuations for a black hole using third quantization. We will demonstrate that these quantum fluctuations depend on the factor ordering chosen. So, we will show that only certain values of the factor ordering parameter are consistent with virtual black holes model of spacetime foam. - Highlights: • We analyze the Wheeler–DeWitt equation using third quantization. • The quantum fluctuations of geometry is studied using this formalism. • These quantum fluctuations produce virtual black holes. • This model is consistent with only certain values of the factor ordering.},

doi = {10.1016/J.AOP.2017.06.020},

journal = {Annals of Physics},

issn = {0003-4916},

number = ,

volume = 384,

place = {United States},

year = {2017},

month = {9}

}