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

We show numerically that the Abelian Higgs field equations in the background of a four-dimensional rotating charged black string have vortex solutions. These solutions which have axial symmetry show that the rotating black string can support the Abelian Higgs field as hair. We find that one encounters with an electric field coupled to the Higgs scalar field for the case of rotating black string. This electric field is due to an electric charge per unit length, which increases...

We analyse vortex hair for charged rotating asymptotically AdS black holes in the abelian Higgs model. We give analytical and numerical arguments to show how the vortex interacts with the horizon of the black hole, and how the solution extends to the boundary. The solution is very close to the corresponding asymptotically flat vortex, once one transforms to a frame that is non-rotating at the boundary. We show that there is a Meissner effect for extremal black holes, with the...

Motivated by the study of holographic superconductors, we generalize no-hair theorems for minimally coupled scalar fields charged under an Abelian gauge field, in arbitrary dimensions and with arbitrary horizon topology. We first present a straightforward generalization of no-hair theorems for neutral scalar hair. We then consider the existence of extremal black holes with scalar hair, and in the case of horizons with zero or positive curvature, provide a bound on the mass an...

We examine the claim of Chamblin et. al. that extreme black holes cannot support abelian Higgs hair. We provide evidence that contradicts this claim and discuss reasons for this discrepancy.

A rotating black hole threaded by an infinitely long cosmic string is studied in the framework of the Abelian Higgs model. We show that contrary to a common belief, in the presence of rotation the backreaction of the string does not induce a simple conical deficit. This leads to new distinct features of the Kerr--string system such as modified ISCO or shifted ergosphere, though these effects are likely outside the range of observational precision. For an extremal rotating bla...

We show that the Abelian Higgs field equations in the background of the four dimensional AdS-Schwarzschild black hole have a vortex line solution. This solution, which has axial symmetry, is a generalization of the AdS spacetime Nielsen-Olesen string. By a numerical study of the field equations, we show that black hole could support the Abelian Higgs field as its Abelian hair. Also, we conside the self gravity of the Abelian Higgs field both in the pure AdS spacetime and AdS-...

Static spherically symmetric asymptotically flat charged black hole solutions are constructed within the magnetic SU(3) sector of the 4-dimensional heterotic string effective action. They possess non-abelian hair in addition to the Coulomb magnetic field and are qualitatively similar to the Einstein-Yang-Mills colored SU(3) black holes except for the extremal case. In the extremality limit the horizon shrinks and the resulting geometry around the origin coincides with that of...

Stationary axisymmetric magnetic fields are expelled from outer horizons of black holes as they become extremal. Extreme black holes exhibit Meissner effect also within exact Einstein--Maxwell theory and in string theories in higher dimensions. Since maximally rotating black holes are expected to be astrophysically most important, the expulsion of the magnetic flux from their horizons represents a potential threat to an electromagnetic mechanism launching the jets at the acco...

We examined analytically and proposed a numerical model of an Abelian Higgs dark matter vortex in the spacetime of a stationary axisymmetric Kerr black hole. In analytical calculations the dark matter sector was modeled by an addition of a U (1)-gauge field coupled to the visible sector. The backreaction analysis revealed that the impact of the dark vortex presence is far more complicated than causing only a deficit angle. The vortex causes an ergosphere shift and the event h...

We argue the existence of solutions of the Euclidean Einstein equations that correspond to a vortex sitting at the horizon of a black hole. We find the asymptotic behaviours, at the horizon and at infinity, of vortex solutions for the gauge and scalar fields in an abelian Higgs model on a Euclidean Schwarzschild background and interpolate between them by integrating the equations numerically. Calculating the backreaction shows that the effect of the vortex is to cut a slice o...