# Asymptotically flat black holes in Horndeski theory and beyond

## Abstract

We find spherically symmetric and static black holes in shift-symmetric Horndeski and beyond Horndeski theories. They are asymptotically flat and sourced by a non trivial static scalar field. The first class of solutions is constructed in such a way that the Noether current associated with shift symmetry vanishes, while the scalar field cannot be trivial. This in certain cases leads to hairy black hole solutions (for the quartic Horndeski Lagrangian), and in others to singular solutions (for a Gauss-Bonnet term). Additionally, we find the general spherically symmetric and static solutions for a pure quartic Lagrangian, the metric of which is Schwarzschild. We show that under two requirements on the theory in question, any vacuum GR solution is also solution to the quartic theory. As an example, we show that a Kerr black hole with a non-trivial scalar field is an exact solution to these theories.

- Authors:

- Laboratoire de Physique Théorique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay (France)

- Publication Date:

- OSTI Identifier:
- 22679913

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 04; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; BLACK HOLES; EXACT SOLUTIONS; LAGRANGIAN FUNCTION; METRICS; SCALAR FIELDS; SIMULATION; SPHERICAL CONFIGURATION; SYMMETRY

### Citation Formats

```
Babichev, E., Charmousis, C., and Lehébel, A., E-mail: eugeny.babichev@th.u-psud.fr, E-mail: christos.charmousis@th.u-psud.fr, E-mail: antoine.lehebel@th.u-psud.fr.
```*Asymptotically flat black holes in Horndeski theory and beyond*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/04/027.

```
Babichev, E., Charmousis, C., & Lehébel, A., E-mail: eugeny.babichev@th.u-psud.fr, E-mail: christos.charmousis@th.u-psud.fr, E-mail: antoine.lehebel@th.u-psud.fr.
```*Asymptotically flat black holes in Horndeski theory and beyond*. United States. doi:10.1088/1475-7516/2017/04/027.

```
Babichev, E., Charmousis, C., and Lehébel, A., E-mail: eugeny.babichev@th.u-psud.fr, E-mail: christos.charmousis@th.u-psud.fr, E-mail: antoine.lehebel@th.u-psud.fr. Sat .
"Asymptotically flat black holes in Horndeski theory and beyond". United States.
doi:10.1088/1475-7516/2017/04/027.
```

```
@article{osti_22679913,
```

title = {Asymptotically flat black holes in Horndeski theory and beyond},

author = {Babichev, E. and Charmousis, C. and Lehébel, A., E-mail: eugeny.babichev@th.u-psud.fr, E-mail: christos.charmousis@th.u-psud.fr, E-mail: antoine.lehebel@th.u-psud.fr},

abstractNote = {We find spherically symmetric and static black holes in shift-symmetric Horndeski and beyond Horndeski theories. They are asymptotically flat and sourced by a non trivial static scalar field. The first class of solutions is constructed in such a way that the Noether current associated with shift symmetry vanishes, while the scalar field cannot be trivial. This in certain cases leads to hairy black hole solutions (for the quartic Horndeski Lagrangian), and in others to singular solutions (for a Gauss-Bonnet term). Additionally, we find the general spherically symmetric and static solutions for a pure quartic Lagrangian, the metric of which is Schwarzschild. We show that under two requirements on the theory in question, any vacuum GR solution is also solution to the quartic theory. As an example, we show that a Kerr black hole with a non-trivial scalar field is an exact solution to these theories.},

doi = {10.1088/1475-7516/2017/04/027},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 04,

volume = 2017,

place = {United States},

year = {Sat Apr 01 00:00:00 EDT 2017},

month = {Sat Apr 01 00:00:00 EDT 2017}

}