# No hair theorem in quasi-dilaton massive gravity

## Abstract

We investigate the static, spherically symmetric black hole solutions in the quasi-dilaton model and its generalizations, which are scalar extended dRGT massive gravity with a shift symmetry. We show that, unlike generic scalar extended massive gravity models, these theories do not admit static, spherically symmetric black hole solutions until the theory parameters in the dRGT potential are fine-tuned. When fine-tuned, the geometry of the static, spherically symmetric black hole is necessarily that of general relativity and the quasi-dilaton field is constant across the spacetime. The fine-tuning and the no hair theorem apply to black holes with flat, anti-de Sitter or de Sitter asymptotics. (C) 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP(3).

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Chinese Academy of Sciences, Beijing (China)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1246701

- Alternate Identifier(s):
- OSTI ID: 1280702

- Grant/Contract Number:
- SC0010600

- Resource Type:
- Published Article

- Journal Name:
- Physics Letters B

- Additional Journal Information:
- Journal Name: Physics Letters B Journal Volume: 757 Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Country of Publication:
- Netherlands

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS

### Citation Formats

```
Wu, De-Jun, and Zhou, Shuang-Yong. No hair theorem in quasi-dilaton massive gravity. Netherlands: N. p., 2016.
Web. doi:10.1016/j.physletb.2016.04.016.
```

```
Wu, De-Jun, & Zhou, Shuang-Yong. No hair theorem in quasi-dilaton massive gravity. Netherlands. doi:10.1016/j.physletb.2016.04.016.
```

```
Wu, De-Jun, and Zhou, Shuang-Yong. Wed .
"No hair theorem in quasi-dilaton massive gravity". Netherlands. doi:10.1016/j.physletb.2016.04.016.
```

```
@article{osti_1246701,
```

title = {No hair theorem in quasi-dilaton massive gravity},

author = {Wu, De-Jun and Zhou, Shuang-Yong},

abstractNote = {We investigate the static, spherically symmetric black hole solutions in the quasi-dilaton model and its generalizations, which are scalar extended dRGT massive gravity with a shift symmetry. We show that, unlike generic scalar extended massive gravity models, these theories do not admit static, spherically symmetric black hole solutions until the theory parameters in the dRGT potential are fine-tuned. When fine-tuned, the geometry of the static, spherically symmetric black hole is necessarily that of general relativity and the quasi-dilaton field is constant across the spacetime. The fine-tuning and the no hair theorem apply to black holes with flat, anti-de Sitter or de Sitter asymptotics. (C) 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP(3).},

doi = {10.1016/j.physletb.2016.04.016},

journal = {Physics Letters B},

number = C,

volume = 757,

place = {Netherlands},

year = {2016},

month = {6}

}

DOI: 10.1016/j.physletb.2016.04.016

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