  We study the stability of (4+1)-dimensional charged Gauss-Bonnet black holes
and solitons. We observe an instability related to the condensation of a scalar
field and construct explicit "hairy" black hole and soliton solutions of the
full system of coupled field equations. We investigate the cases of a massless
scalar field as well as that of a tachyonic scalar field. The solitons with
scalar hair exist for a particular range of the charge and the gauge coupling.
This range is such that for intermediate values of the gauge coupling a
"forbidden band" of charges for the hairy solitons exists. We also discuss the
behaviour of the black holes with scalar hair when changing the horizon radius
and/or the gauge coupling and find that various scenarios at the approach of a
limiting solution appear. One observation is that hairy Gauss-Bonnet black
holes never tend to a regular soliton solution in the limit of vanishing
horizon radius. We also prove that extremal Gauss-Bonnet black holes can not
carry massless or tachyonic scalar hair and show that our solutions tend to
their planar counterparts for large charges.
