Scalar Hair of Global Defect and Black Brane World

Abstract

We consider a complex scalar field in (p + 3)-dimensional bulk with a negative cosmological constant and study global vortices in two extra-dimensions. We reexamine carefully the coupled scalar and Einstein equations, and show that the boundary value of scalar amplitude at infinity of the extra-dimensions should be smaller than vacuum expectation value. The brane world has a cigar-like geometry with an exponentially decaying warp factor and a flat thick p-brane is embedded. Since a coordinate transformation identifies the obtained brane world as a black p-brane world bounded by a horizon, this strange boundary condition of the scalar amplitude is understood as existence of a short scalar hair.