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We show that a black hole surrounded by scalar dark matter develops scalar hair. This is the generalization of a phenomenon pointed out by Jacobson, that a minimally coupled scalar with a non-trivial time dependence far away from the black hole would endow the black hole with hair. In our case, the time dependence arises from the oscillation of a scalar field with a non-zero mass. We systematically explore the scalar profile around the black hole for different scalar masses. In the small mass limit, the scalar field has a $1/r$ component at large radius $r$, consistent with Jacobsons result. In the large mass limit (with the Compton wavelength of order of the horizon or smaller), the scalar field has a $1/r^{3/4}$ profile yielding a pile-up close to the horizon, while distinctive nodes occur for intermediate masses. Thus, the dark matter profile around a black hole, while challenging to measure, contains information about the dark matter particle mass. As an application, we consider the case of the supermassive black hole at the center of M87, recently imaged by the Event Horizon Telescope. Its horizon size is roughly the Compton wavelength of a scalar particle of mass $10^{-20}$ eV. We consider the implications of the expected scalar pile-up close to the horizon, for fuzzy dark matter at a mass of $10^{-20}$ eV or below.
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Scalar fields around compact objects are of interest for scalar-tensor theories of gravity and dark matter models consisting of a massive scalar, e.g. axions. We study the behaviour of a scalar field around a Kerr black hole with non trivial asymptotic boundary conditions - both non zero density and non zero angular momentum. Starting from an initial radially homogeneous configuration, a scalar cloud is accreted, which asymptotes to known stationary configurations over time. We study the cloud growth for different parameters including black hole spin, scalar field mass, and the scalar field density and angular momentum far from the black hole. We characterise the transient growth of the mass and angular momentum in the cloud, and the spatial profile of the scalar around the black hole, and relate the results of fully non-linear simulations to an analytic perturbative expansion. We also highlight the potential for these accreted clouds to create monochromatic gravitational wave signals - similar to the signals from superradiant clouds, although significantly weaker in amplitude.
Light bosonic scalars (e.g. axions) may form clouds around black holes via superradiant instabilities, or via accretion if they form some component of the dark matter. It has been suggested that their presence may lead to a distinctive dephasing of the gravitational wave signal when a small compact object spirals into a larger black hole. Motivated by this, we study numerically the dynamical friction force on a black hole moving at relativistic velocities in a background scalar field with an asymptotically homogeneous energy density. We show that the relativistic scaling is analogous to that found for supersonic collisional fluids, assuming an approximate expression for the pressure correction which depends on the velocity and scalar mass. While we focus on a complex scalar field, our results confirm the expectation that real scalars would exert a force which oscillates between positive and negative values in time with a frequency set by the scalar mass. The complex field describes the time averaged value of this force, but in a real scalar the rapid force oscillations could in principle leave an imprint on the trajectory. The approximation we obtain can be used to inform estimates of dephasing in the final stages of an extreme mass ratio inspiral.
We revisit the physical effects of discrete $mathbb{Z}_p$ gauge charge on black hole thermodynamics, building on the seminal work of Coleman, Preskill, and Wilczek. Realising the discrete theory from the spontaneous breaking of an Abelian gauge theory, we consider the two limiting cases of interest, depending on whether the Compton wavelength of the massive vector is much smaller or much larger than the size of the black hole -- the so-called thin- and thick-string limits respectively. We find that the qualitative effect of discrete hair on the mass-temperature relationship is the same in both regimes, and similar to that of unbroken $U(1)$ charge: namely, a black hole carrying discrete gauge charge is always colder than its uncharged counterpart. In the thick-string limit, our conclusions bring into question some of the results of Coleman et al., as we discuss. Further, by considering the system to be enclosed within a finite cavity, we argue how the unbroken limit may be smoothly defined, and the unscreened electric field of the standard Reissner-Nordstrom solution recovered.
For the first time, we obtain the analytical form of black hole space-time metric in dark matter halo for the stationary situation. Using the relation between the rotation velocity (in the equatorial plane) and the spherical symmetric space-time metric coefficient, we obtain the space-time metric for pure dark matter. By considering the dark matter halo in spherical symmetric space-time as part of the energy-momentum tensors in the Einstein field equation, we then obtain the spherical symmetric black hole solutions in dark matter halo. Utilizing Newman-Jains method, we further generalize spherical symmetric black holes to rotational black holes. As examples, we obtain the space-time metric of black holes surrounded by Cold Dark Matter and Scalar Field Dark Matter halos, respectively. Our main results regarding the interaction between black hole and dark matter halo are as follows: (i) For both dark matter models, the density profile always produces cusp phenomenon in small scale in the relativity situation; (ii) Dark matter halo makes the black hole horizon to increase but the ergosphere to decrease, while the magnitude is small; (iii) Dark matter does not change the singularity of black holes. These results are useful to study the interaction of black hole and dark matter halo in stationary situation. Particularly, the cusp produced in the $0sim 1$ kpc scale would be observable in the Milky Way. Perspectives on future work regarding the applications of our results in astrophysics are also briefly discussed.
Searching for violations of the no-hair theorem (NHT) is a powerful way to test gravity, and more generally fundamental physics, particularly with regards to the existence of additional scalar fields. The first observation of a black hole (BH) shadow by the Event Horizon Telescope (EHT) has opened a new direct window onto tests of gravity in the strong-field regime, including probes of violations of the NHT. We consider two scenarios described by the Einstein-Maxwell equations of General Relativity and electromagnetism, to which we add a scalar field. In the first case we consider a minimally-coupled scalar field with a potential, whereas in the second case the field is conformally-coupled to curvature. In both scenarios we construct charged BH solutions, which are found to carry primary scalar hair. We then compute the shadows cast by these two BHs as a function of their electric charge and scalar hair parameter. Comparing these shadows to the shadow of M87* recently imaged by the EHT collaboration, we set constraints on the amount of scalar hair carried by these two BHs. The conformally-coupled case admits a regime for the hair parameter, compatible with EHT constraints, describing a so-called mutated Reissner-Nordstr{o}m BH: this solution was recently found to effectively mimic a wormhole. Our work provides novel constraints on fundamental physics, and in particular on violations of the no-hair theorem and the existence of additional scalar fields, from the shadow of M87*.
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