## Abstract

We consider Kaluza–Klein models where internal spaces are compact flat or curved Einstein spaces. This background is perturbed by a compact gravitating body with the dust-like equation of state (EoS) in the external/our space and an arbitrary EoS parameter Ω in the internal space. Without imposing any restrictions on the form of the perturbed metric and the distribution of the perturbed energy densities, we perform the general analysis of the Einstein and conservation equations in the weak-field limit. All conclusions follow from this analysis. For example, we demonstrate that the perturbed model is static and perturbed metric preserves the block-diagonal form. In a particular case Ω=−1/2, the found solution corresponds to the weak-field limit of the black strings/branes. The black strings/branes are compact gravitating objects which have the topology (four-dimensional Schwarzschild spacetime) × (d-dimensional internal space) with d≥1. We present the arguments in favour of these objects. First, they satisfy the gravitational tests for the parameterized post-Newtonian parameter γ at the same level of accuracy as General Relativity. Second, they are preferable from the thermodynamical point of view. Third, averaging over the Universe, they do not destroy the stabilization of the internal space. These are the astrophysical and cosmological aspects of the black strings/branes.

Original language | English |
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Pages (from-to) | 190-196 |

Number of pages | 7 |

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

Volume | 778 |

DOIs | |

Publication status | Published - 10 Mar 2018 |

### Bibliographical note

Publisher Copyright:© 2018 The Author(s)

### Funding

ÖA acknowledges the support by the Distinguished Young Scientist Award BAGEP of the Science Academy. AZ acknowledges financial support from the Scientific and Technological Research Council of Turkey (TUBITAK) in the scheme of Fellowships for Visiting Scientists and Scientists on Sabbatical Leave (BIDEB 2221). AZ also acknowledges the hospitality of İstanbul Technical University (ITU) where parts of this work were carried out. The authors are grateful to Maxim Eingorn for stimulating discussions and valuable comments. ÖA acknowledges the support by the Distinguished Young Scientist Award BAGEP of the Science Academy . AZ acknowledges financial support from the Scientific and Technological Research Council of Turkey (TUBITAK) in the scheme of Fellowships for Visiting Scientists and Scientists on Sabbatical Leave ( BIDEB 2221 ). AZ also acknowledges the hospitality of İstanbul Technical University (ITU) where parts of this work were carried out. The authors are grateful to Maxim Eingorn for stimulating discussions and valuable comments.

Funders | Funder number |
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TUBITAK | |

Academy of Health Sciences | |

Türkiye Bilimsel ve Teknolojik Araştirma Kurumu | BIDEB 2221 |

National Council for Scientific Research | |

Bilim Akademisi |

## Keywords

- Black strings/branes
- Einstein spaces
- Gravitational tests
- Kaluza–Klein models
- Multidimensional models
- Weak-field limit