Scalar Hair of Global Defect and Black Brane World

TL;DR

This paper investigates scalar field configurations in higher-dimensional spacetimes, revealing that scalar hair can exist on black brane worlds with a cigar-like geometry, challenging traditional boundary conditions.

Contribution

It demonstrates the existence of scalar hair in black brane world scenarios with specific boundary conditions, providing new insights into scalar field behavior in higher dimensions.

Findings

Scalar amplitude boundary value must be smaller than vacuum expectation value

The brane world has a cigar-like geometry with exponential warp factor

Existence of scalar hair on black p-brane world bounded by a horizon

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.