Weyl invariant black hole

The properties of the Weyl invariant black hole and its implications are studied. The calculation shows that there is no hair, up to a gauge choice, for a Weyl gauge field outside the event horizon of a black hole in the Weyl invariant limit. We also show that a scalar field will remain constant once the scale symmetry is broken spontaneously by the well-known Higgs potential. As a result, classical hair for the Weyl vector meson and scalar measuring field vanishes strictly in the presence of a spontaneously symmetry-breaking potential. Hence the no-hair theorem holds both in the Weyl invariant limit and the symmetry-breaking phase.