### Abstract

The generalized Proca theories with second-order equations of motion can be healthily extended to a more general framework in which the number of propagating degrees of freedom remains unchanged. In the presence of a quartic-order nonminimal coupling to gravity arising in beyond-generalized Proca theories, the speed of gravitational waves c_{t} on the Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological background can be equal to that of light c under a certain condition. By using this condition alone, we show that the speed of gravitational waves in the vicinity of static and spherically symmetric black holes is also equivalent to c for the propagation of odd-parity perturbations along both radial and angular directions. As a by-product, the black holes arising in our beyond-generalized Proca theories are plagued by neither ghost nor Laplacian instabilities against odd-parity perturbations. We show the existence of both exact and numerical black hole solutions endowed with vector hairs induced by the quartic-order coupling.

Original language | English |
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Pages (from-to) | 541-550 |

Number of pages | 10 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 782 |

DOIs | |

Publication status | Published - 2018 Jul 10 |

Externally published | Yes |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*,

*782*, 541-550. https://doi.org/10.1016/j.physletb.2018.05.078