## Abstract

We consider spherically symmetric higher-dimensional solutions of Einstein's equations with a bulk cosmological constant and n transverse dimensions. In contrast to the case of one or two extra dimensions we find no solutions that localize gravity when n ≥ 3, for strictly local topological defects. We discuss global topological defects that lead to the localization of gravity and estimate the corrections to Newton's law. We show that the introduction of a bulk 'hedgehog' magnetic field leads to a regular geometry and localizes gravity on the 3-brane with either a positive, zero or negative bulk cosmological constant. The corrections to Newton's law on the 3-brane are parametrically the same as for the case of one transverse dimension.

Original language | English (US) |
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Pages (from-to) | 353-361 |

Number of pages | 9 |

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

Volume | 491 |

Issue number | 3-4 |

DOIs | |

State | Published - Oct 19 2000 |

### Bibliographical note

Funding Information:We wish to thank E. Poppitz, S. Randjbar-Daemi, P. Tinyakov and V. Rubakov for helpful discussions. This work was supported by the FNRS, contract no. 21-55560.98.