Explore the vast range of titles available.

The asymptotically flat, spherical, electro-vacuum black holes (BHs) are shown to support static, spherical configurations of a gauged, self-interacting, scalar field, minimally coupled to the geometry. Considering a Q -ball type potential for the scalar field, we dub these configurations Q - clouds , in the test field approximation. The clouds exist under a resonance condition , at the threshold of (charged) superradiance. This is similar to the stationary clouds supported by Kerr BHs, which exist for a synchronisation condition , at the threshold of (rotational) superradiance. In contrast with the rotating case, however, Q -clouds require the scalar field to be massive and self-interacting; no similar clouds exist for massive but free scalar fields. First, considering a decoupling limit, we construct Q -clouds around Schwarzschild and Reissner–Nordström BHs, showing there is always a mass gap. Then, we make the Q -clouds backreact, and construct fully non-linear solutions of the Einstein–Maxwell-gauged scalar system describing spherical, charged BHs with resonant, scalar Q - hair . Amongst other properties, we observe there is non-uniqueness of charged BHs in this model and the Q -hairy BHs can be entropically preferred over Reissner–Nordström, for the same charge to mass ratio; some Q -hairy BH solutions can be overcharged. We also discuss how some well known no-hair theorems in the literature, applying to electro-vacuum plus minimally coupled scalar fields, are circumvented by this new type of BHs.

Einstein–Maxwell-scalar models allow for different classes of black hole solutions, depending on the non-minimal coupling function f(ϕ) employed, between the scalar field and the Maxwell invariant. Here, we address the linear mode stability of the black hole solutions obtained recently for a quartic coupling function, f(ϕ)=1+αϕ4 (Blázquez-Salcedo et al. in Phys. Lett. B 806:135493, 2020). Besides the bald Reissner–Nordström solutions, this coupling allows for two branches of scalarized black holes, termed cold and hot, respectively. For these three branches of black holes we calculate the spectrum of quasinormal modes. It consists of polar scalar-led modes, polar and axial electromagnetic-led modes, and polar and axial gravitational-led modes. We demonstrate that the only unstable mode present is the radial scalar-led mode of the cold branch. Consequently, the bald Reissner–Nordström branch and the hot scalarized branch are both mode-stable. The non-trivial scalar field in the scalarized background solutions leads to the breaking of the degeneracy between axial and polar modes present for Reissner–Nordström solutions. This isospectrality is only slightly broken on the cold branch, but it is strongly broken on the hot branch.

For ultra compact objects, light rings and fundamental photon orbits (FPOs) play a pivotal role in the theoretical analysis of strong gravitational lensing effects, and of BH shadows in particular. In this short review, specific models are considered to illustrate how FPOs can be useful in order to understand some non-trivial gravitational lensing effects. This paper aims at briefly overviewing the theoretical foundations of these effects, touching also some of the related phenomenology, both in general relativity and alternative theories of gravity, hopefully providing some intuition and new insights for the underlying physics, which might be critical when testing the Kerr black hole hypothesis.

Hypothetical ultralight bosonic fields will spontaneously form macroscopic bosonic halos around Kerr black holes, via superradiance, transferring part of the mass and angular momentum of the black hole into the halo. Such a process, however, is only efficient if resonant—when the Compton wavelength of the field approximately matches the gravitational scale of the black hole. For a complex-valued field, the process can form a stationary, bosonic field black hole equilibrium state—a black hole with synchronised hair. For sufficiently massive black holes, such as the one at the centre of the M87 supergiant elliptic galaxy, the hairy black hole can be robust against its own superradiant instabilities, within a Hubble time. Studying the shadows of such scalar hairy black holes, we constrain the amount of hair which is compatible with the Event Horizon Telescope (EHT) observations of the M87 supermassive black hole, assuming the hair is a condensate of ultralight scalar particles of mass μ ∼ 10 − 20 eV, as to be dynamically viable. We show the EHT observations set a weak constraint, in the sense that typical hairy black holes that could develop their hair dynamically, are compatible with the observations, when taking into account the EHT error bars and the black hole mass/distance uncertainty.

Recently, no-go theorems for the existence of solitonic solutions in Einstein–Maxwell-scalar (EMS) models have been established (Herdeiro and Oliveira in Class Quantum Gravity 36(10):105015, 2019 ). Here we discuss how these theorems can be circumvented by a specific class of non-minimal coupling functions between a real, canonical scalar field and the electromagnetic field. When the non-minimal coupling function diverges in a specific way near the location of a point charge, it regularises all physical quantities yielding an everywhere regular, localised lump of energy. Such solutions are possible even in flat spacetime Maxwell-scalar models, wherein the model is fully integrable in the spherical sector, and exact solutions can be obtained, yielding an explicit mechanism to de-singularise the Coulomb field. Considering their gravitational backreaction, the corresponding (numerical) EMS solitons provide a simple example of self-gravitating, localised energy lumps.

Obtaining solutions of the Einstein field equations describing spinning compact bodies is typically challenging. The Newman–Janis algorithm provides a procedure to obtain rotating spacetimes from a static, spherically symmetric, seed metric. It is not guaranteed, however, that the resulting rotating spacetime solves the same field equations as the seed. Moreover, the former may not be circular, and thus expressible in Boyer–Lindquist-like coordinates. Amongst the variations of the original procedure, a modified Newman–Janis algorithm (MNJA) has been proposed that, by construction, originates a circular, spinning spacetime, expressible in Boyer–Lindquist-like coordinates. As a down side, the procedure introduces an ambiguity, that requires extra assumptions on the matter content of the model. In this paper we observe that the rotating spacetimes obtained through the MNJA always admit separability of the Hamilton–Jacobi equation for the case of null geodesics, in which case, moreover, the aforementioned ambiguity has no impact, since it amounts to an overall metric conformal factor. We also show that the Hamilton–Jacobi equation for light rays propagating in a plasma admits separability if the plasma frequency obeys a certain constraint. As an illustration, we compute the shadow and lensing of some spinning black holes obtained by the MNJA.

A bstract Einstein-Maxwell theory has powerful solution generating techniques which include Harrison transformations in the Ernst formalism. We construct generalised Harrison transformations that preserve the purely magnetic or purely electric sector in Einstein-ModMax (EMM) theory. Thus, they serve as solution generating techniques within these sectors for this model of non-linear electrodynamics minimally coupled to gravity. As an application we rederive several known exact solutions of EMM and a new solution, black diholes, describing two extremal BHs in equilibrium, with opposite magnetic charges, whose attraction is balanced by their embedding in the Melvin magnetic universe of this model. As a further generalisation, we consider Einstein-dilaton-ModMax theory, and provide the extremal charged BHs and black diholes also in this model.

A bstract We construct spinning black holes (BHs) in shift-symmetric Horndeski theory. This is an Einstein-scalar-Gauss-Bonnet model wherein the (real) scalar field couples linearly to the Gauss-Bonnet curvature squared combination. The BH solutions constructed are stationary, axially symmetric and asymptotically flat. They possess a non-trivial scalar field outside their regular event horizon; thus they have scalar hair. The scalar “charge” is not, however, an independent macroscopic degree of freedom. It is proportional to the Hawking temperature, as in the static limit, wherein the BHs reduce to the spherical solutions found by Sotirou and Zhou. The spinning BHs herein are found by solving non-perturbatively the field equations, numerically. We present an overview of the parameter space of the solutions together with a study of their basic geometric and phenomenological properties. These solutions are compared with the spinning BHs in the Einstein-dilaton-Gauss-Bonnet model and the Kerr BH of vacuum General Relativity. As for the former, and in contrast with the latter, there is a minimal BH size and small violations of the Kerr bound. Phenomenological differences with respect to either the former or the latter, however, are small for illustrative observables, being of the order of a few percent, at most.

A bstract Recent studies have made key progress on the black hole/solitonic solutions of the Einstein-Proca system. Firstly, fully non-linear dynamical evolutions of the Kerr black hole superradiant instability, triggered by a Proca field, have shown the formation of a new equilibrium state, a spinning black hole with synchronised Proca hair. Secondly, non-linear evolutions of spinning Proca stars have established that they are dynamically stable, unlike their scalar cousins. Thirdly, separability of the Proca equation on the Kerr background has been achieved. Motivated by these results, in this paper we reconsider Kerr black holes with synchronised Proca hair. The separability of the Proca equation on the Kerr background allows us to examine the stationary Proca clouds in greater detail, in particular their dependence on the different quantum numbers. These stationary clouds occur at a set of existence lines in the Kerr parameter space, from which the black holes with synchronised Proca hair bifurcate. We construct the domain of existence of these black holes, comparing the fundamental states missed in the original study with the first excited states and with the cousin scalar model, giving illustrative examples of Kerr-like and non- Kerr-like BHs. In the vanishing event horizon limit, these hairy black holes connect to the fundamental states of spinning Proca stars, which include the dynamically stable solutions.

We consider the minimally coupled Klein-Gordon equation for a charged, massive scalar field in the non-extremal Reissner-Nordström background. Performing a frequency domain analysis, using a continued fraction method, we compute the frequencies ω for quasi-bound states. We observe that, as the extremal limit for both the background and the field is approached, the real part of the quasi-bound states frequencies R(ω) tends to the mass of the field and the imaginary part I(ω) tends to zero, for any angular momentum quantum number ℓ . The limiting frequencies in this double extremal limit are shown to correspond to a distribution of extremal scalar particles, at stationary positions, in no-force equilibrium configurations with the background. Thus, generically, these stationary scalar configurations are regular at the event horizon. If, on the other hand, the distribution contains scalar particles at the horizon, the configuration becomes irregular therein, in agreement with no hair theorems for the corresponding Einstein-Maxwell-scalar field system.