Narrow Results

As an alternative to the “no hair conjecture,” the “no short hair conjecture” for hairy black holes was established earlier. This theorem stipulates that hair must be present above 3/2 of the event horizon radius for a hairy black hole. It is assumed that the nonlinear behavior of the matter field plays a key role in the presence of such hair. Subsequently, it was established that the hair must extend beyond the photon sphere of the corresponding black hole. We have investigated the validity of the “no short hair conjecture” in pure Lovelock gravity. Our analysis has shown that irrespective of dimensionality and Lovelock order, the hair of a static, spherically symmetric black hole extends at least up to the photon sphere.

We show that scalar hair can be added to rotating, vacuum black holes (BHs) of general relativity. These hairy black holes (HBHs) clarify a lingering question concerning gravitational solitons: Whether a BH can be added at the centre of a boson star (BS), as it typically can for other solitons. We argue that it can, but only if it is spinning. The existence of such HBHs is related to the Kerr superradiant instability triggered by a massive scalar field. This connection leads to the following conjecture: a (hairless) BH, which is afflicted by the superradiant instability of a given field, must allow hairy generalizations with that field.

The gravitational description of black hole microstructure via the fuzzball proposal suggests a vast space of solutions called fuzzballs. This idea together with the 4d and 5d microscopic counting formulas necessitates that each supersymmetric 4d fuzzball admits an infinite number of hair. The hair removed fuzzballs are the true horizon degrees of freedom. We discuss how to construct/identify, count, and remove fuzzball hair.