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)|
|Number of pages||9|
|Journal||Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics|
|State||Published - Oct 19 2000|
Bibliographical noteFunding 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.