# Non-singular black holes in massive gravity: time-dependent solutions

## Abstract

When starting with a static, spherically-symmetric ansatz, there are two types of black hole solutions in dRGT massive gravity: (i) exact Schwarzschild solutions which exhibit no Yukawa suppression at large distances and (ii) solutions in which the dynamical metric and the reference metric are simultaneously diagonal and which inevitably exhibit coordinate-invariant singularities at the horizon. In this work we investigate the possibility of black hole solutions which can accommodate both a nonsingular horizon and Yukawa asymptotics. In particular, by adopting a time-dependent ansatz, we derive perturbative analytic solutions which possess non-singular horizons. These black hole solutions are indistinguishable from Schwarzschild black holes in the limit of zero graviton mass. At finite graviton mass, they depend explicitly on time. However, we demonstrate that the location of the apparent horizon is not necessarily time-dependent, indicating that these black holes are not necessarily accreting or evaporating (classically). Thus in deriving these results, we also review and extend known results about static black hole solutions in massive gravity.

- Authors:

- Columbia Univ., New York, NY (United States)

- Publication Date:

- Research Org.:
- Columbia Univ., New York, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1499156

- Grant/Contract Number:
- SC0011941

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 10; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTRONOMY AND ASTROPHYSICS; Black Holes; Classical Theories of Gravity; Effective Field Theories

### Citation Formats

```
Rosen, Rachel A. Non-singular black holes in massive gravity: time-dependent solutions. United States: N. p., 2017.
Web. doi:10.1007/jhep10(2017)206.
```

```
Rosen, Rachel A. Non-singular black holes in massive gravity: time-dependent solutions. United States. doi:10.1007/jhep10(2017)206.
```

```
Rosen, Rachel A. Mon .
"Non-singular black holes in massive gravity: time-dependent solutions". United States. doi:10.1007/jhep10(2017)206. https://www.osti.gov/servlets/purl/1499156.
```

```
@article{osti_1499156,
```

title = {Non-singular black holes in massive gravity: time-dependent solutions},

author = {Rosen, Rachel A.},

abstractNote = {When starting with a static, spherically-symmetric ansatz, there are two types of black hole solutions in dRGT massive gravity: (i) exact Schwarzschild solutions which exhibit no Yukawa suppression at large distances and (ii) solutions in which the dynamical metric and the reference metric are simultaneously diagonal and which inevitably exhibit coordinate-invariant singularities at the horizon. In this work we investigate the possibility of black hole solutions which can accommodate both a nonsingular horizon and Yukawa asymptotics. In particular, by adopting a time-dependent ansatz, we derive perturbative analytic solutions which possess non-singular horizons. These black hole solutions are indistinguishable from Schwarzschild black holes in the limit of zero graviton mass. At finite graviton mass, they depend explicitly on time. However, we demonstrate that the location of the apparent horizon is not necessarily time-dependent, indicating that these black holes are not necessarily accreting or evaporating (classically). Thus in deriving these results, we also review and extend known results about static black hole solutions in massive gravity.},

doi = {10.1007/jhep10(2017)206},

journal = {Journal of High Energy Physics (Online)},

number = 10,

volume = 2017,

place = {United States},

year = {2017},

month = {10}

}

*Citation information provided by*

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Web of Science

#### Figures / Tables:

*g*

_{00}(

*r*) component of the metric for black holes in minimal massive gravity (dark gray) and Schwarzschild black holes (light gray).

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*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*