Can extreme black holes have (long) Abelian Higgs hair?

We construct static and axially symmetric magnetically charged hairy black holes in the gravity-coupled Weinberg-Salam theory. Large black holes merge with the Reissner-Nordstr\"om (RN) family, while the small ones are extremal and support a hair in the form of a ring-shaped electroweak condensate carrying superconducting W-currents and up to $22\%$ of the total magnetic charge. The extremal solutions are asymptotically RN with a mass {\it below} the total charge, $M<|Q|$, du...

We briefly summarise the basic properties of spacetimes representing rotating, charged black holes in strong axisymmetric magnetic fields. We concentrate on extremal cases, for which the horizon surface gravity vanishes. We investigate their properties by finding simpler spacetimes that exhibit their geometries near degenerate horizons. Employing the simpler geometries obtained by near-horizon limiting description we analyse the Meissner effect of magnetic field expulsion fro...

Recent developments in string theory have brought forth a considerable interest in time-dependent hair on extended objects. This novel new hair is typically characterized by a wave profile along the horizon and angular momentum quantum numbers $l,m$ in the transverse space. In this work, we present an extensive treatment of such oscillating black objects, focusing on their geometric properties. We first give a theorem of purely geometric nature, stating that such wavy hair ca...

I discuss a recent analytic proof of bypassing the no-hair conjecture for two interesting (and quite generic) cases of four-dimensional black holes: (i) black holes in Einstein-Yang-Mills-Higgs (EYMH) systems and (ii) black holes in higher-curvature (Gauss-Bonnet (GB) type) string-inspired gravity. Both systems are known to possess black-hole solutions with non-trivial scalar hair outside the horizon. The `spirit' of the no-hair conjecture, however, seems to be maintained eit...

While extreme black hole spacetimes with smooth horizons are known at the level of mathematics, we argue that the horizons of physical extreme black holes are effectively singular. Test particles encounter a singularity the moment they cross the horizon, and only objects with significant back-reaction can fall across a smooth (now non-extreme) horizon. As a result, classical interior solutions for extreme black holes are theoretical fictions that need not be reproduced by any...

Spherically symmetric magnetic and dyonic black holes with a magnetic charge $Q=2$ are studied in the Standard Model and general relativity. A magnetically charged black hole with mass below $9.3\times 10^{35}$ GeV has a "hairy" cloud of electroweak gauge and Higgs fields outside the event horizon with $1/m_W$ in size. An extremal magnetic black hole has a hair mass of 3.6 TeV, while an extremal dyonic black hole has an additional mass of $q^2 \times 1.6$ GeV for a small elec...

It is known that the Meissner-like effect is seen in a magnetosphere without an electric current in black hole spacetime: no non-monopole component of magnetic flux penetrates the event horizon if the black hole is extreme. In this paper, in order to see how an electric current affects the Meissner-like effect, we study a force-free electromagnetic system in a static and spherically symmetric extreme black hole spacetime. By assuming that the rotational angular velocity of th...

In the realm of spacetimes governed by Einstein's general relativity and containing only Maxwell's electromagnetic field, stationary black holes are fully characterized by their mass, electric or magnetic charge, and angular momentum -- a property encapsulated in a version of the no-hair theorem. However, the validity of this theorem is contingent on certain assumptions, and when these are relaxed, new solutions describing hairy black holes arise. To date, astronomical observ...

We consider $d\geqslant 4$ Einstein--(extended-)Yang-Mills theory, where the gauge sector is augmented by higher order terms. Linearizing the (extended) Yang-Mills equations on the background of the electric Reissner-Nordstr\"om (RN) black hole, we show the existence of normalizable zero modes, dubbed non-Abelian magnetic stationary clouds. The non-linear realization of these clouds bifurcates the RN family into a branch of static, spherically symmetric, electrically charged ...

We study regular and black hole solutions to the coupled classical Einstein--Yang-Mills--Higgs system. It has long been thought that black hole solutions in the spontaneously broken phase of such a theory could have no nontrivial field structure outside of the horizon. We first show that the standard black hole no-hair theorem underlying this belief, although true in the abelian setting, does not necessarily extend to the non-abelian case. This indicates the possibility of so...