Stationary Clouds Research Articles

Spinning Kerr black holes with stationary massive scalar clouds: the large-coupling regime

We study analytically the Klein-Gordon wave equation for stationary massive scalar fields linearly coupled to spinning Kerr black holes. In particular, using the WKB approximation, we derive a compact formula for the discrete spectrum of scalar field masses which characterize the stationary composed Kerr-black-hole-massive-scalar-field configurations in the large-coupling regime M μ ≫ 1 (here M and μ are respectively the mass of the central black hole and the proper mass of the scalar field). We confirm our analytically derived formula for the Kerr-scalar-field mass spectrum with numerical data that recently appeared in the literature.

Stationary charged scalar clouds around black holes in string theory

It was reported that Kerr-Newman black holes can support linear charged scalar fields in their exterior regions. These stationary massive charged scalar fields can form bound states, which are called stationary scalar clouds. In this paper, we show that Kerr-Sen black holes can also support stationary massive charged scalar clouds by matching the near- and far-region solutions of the radial part of the Klein-Gordon wave equation. We also review stationary scalar clouds within the background of static electrically charged black hole solutions in the low-energy limit of heterotic string field theory, namely, the Gibbons-Maeda-Garfinkle-Horowitz-Strominger black holes.

Kerr black holes with Proca hair

Bekenstein proved that in Einstein's gravity minimally coupled to one (or many) real, Abelian, Proca field, stationary black holes (BHs) cannot have Proca hair. Dropping Bekenstein's assumption that matter inherits spacetime symmetries, we show this model admits asymptotically flat, stationary, axi-symmetric, regular on and outside an event horizon BHs with Proca hair, for an even number of real (or an arbitrary number of complex) Proca fields. To establish it, we start by showing that a test, complex Proca field can form bound states, with real frequency, around Kerr BHs: stationary Proca clouds. These states exist at the threshold of superradiance. It was conjectured in [, ], that the existence of such clouds at the linear level implies the existence of a new family of BH solutions at the nonlinear level. We confirm this expectation and explicitly construct examples of such Kerr BHs with Proca hair (KBHsPH). For a single complex Proca field, these BHs form a countable number of families with three continuous parameters (ADM mass, ADM angular momentum and Noether charge). They branch off from the Kerr solutions that can support stationary Proca clouds and reduce to Proca stars [] when the horizon size vanishes. We present the domain of existence of one family of KBHsPH, as well as its phase space in terms of ADM quantities. Some physical properties of the solutions are discussed; in particular, and in contrast with Kerr BHs with scalar hair, some spacetime regions can be counter-rotating with respect to the horizon. We further establish a no-Proca-hair theorem for static, spherically symmetric BHs but allowing the complex Proca field to have a harmonic time dependence, which shows BHs with Proca hair in this model require rotation and have no static limit. KBHsPH are also disconnected from Kerr–Newman BHs with a real, massless vector field.

Maxwell perturbations on Kerr–anti–de Sitter black holes: Quasinormal modes, superradiant instabilities, and vector clouds

Scalar and gravitational perturbations on Kerr-anti-de Sitter (Kerr-AdS) black holes have been addressed in the literature and have been shown to exhibit a rich phenomenology. In this paper we complete the analysis of bosonic fields on this background by studying Maxwell perturbations, focusing on superradiant instabilities and vector clouds. For this purpose, we solve the Teukolsky equations numerically, imposing the boundary conditions we have proposed in\cite{Wang:2015goa} for the radial Teukolsky equation. As found therein, two Robin boundary conditions can be imposed for Maxwell fields on Kerr-AdS black holes, one of which produces a new set of quasinormal modes even for Schwarzschild-AdS black holes. Here, we show these different boundary conditions produce two different sets of superradiant modes. Interestingly the "new modes" may be unstable in a larger parameter space. We then study stationary Maxwell clouds, that exist at the threshold of the superradiant instability, with the two Robin boundary conditions. These clouds, obtained at the linear level, indicate the existence of a new family of black hole solutions at the nonlinear level, within the Einstein-Maxwell-AdS system, branching off from the Kerr-Newman-AdS family. As a comparison with the Maxwell clouds, scalar clouds on Kerr-AdS black holes are also studied, and it is shown there are Kerr-AdS black holes that are stable against scalar, but not vector modes, with the same "quantum numbers".

The large-mass limit of cloudy black holes

The interplay between black holes and fundamental fields has attracted much attention over the years from both physicists and mathematicians. In this paper we study analytically a physical system that is composed of massive scalar fields linearly coupled to a rapidly rotating Kerr black hole. Using simple arguments, we first show that the coupled black hole-scalar field system may possess stationary bound-state resonances (stationary scalar ‘clouds’) in the bounded regime , where μ and m are respectively the mass and azimuthal harmonic index of the field, and is the angular velocity of the black-hole horizon. We then show explicitly that these two bounds on the dimensionless ratio can be saturated in the asymptotic limit. In particular, we derive a remarkably simple analytical formula for the resonance mass spectrum of the stationary bound-state scalar clouds in the regime of large field masses: , where τ is the dimensionless temperature of the rapidly rotating (near extremal) black hole, is a constant, and is the resonance parameter. In addition, it is shown that, contrary to the flat-space intuition, the effective lengths of the scalar field configurations in the curved black-hole spacetime approach a finite asymptotic value in the large mass limit. In particular, we prove that in the large mass limit, the characteristic length scale of the scalar clouds scales linearly with the black-hole temperature.

Kerr-Newman black holes with stationary charged scalar clouds

It is shown that Kerr-Newman black holes can support linear charged scalar fields in their exterior regions. To that end, we solve analytically the Klein-Gordon wave equation for a stationary charged massive scalar field in the background of a near-extremal Kerr-Newman black hole. In particular, we derive a simple analytical formula which describes the physical properties of these stationary bound-state resonances of the charged massive scalar fields in the Kerr-Newman black-hole spacetime.

Erratum: Stationary scalar clouds around rotating black holes [Phys. Rev. D86, 104026 (2012)

Erratum: Stationary scalar clouds around rotating black holes [Phys. Rev. D<b>86</b>, 104026 (2012)

Stationary scalar clouds around rotating black holes

Motivated by novel results in the theory of wave dynamics in black-hole spacetimes, we analyze the dynamics of a massive scalar field surrounding a rapidly rotating Kerr black hole. In particular, we report on the existence of stationary (infinitely long-lived) regular field configurations in the background of maximally rotating black holes. The effective height of these scalar ``clouds'' above the central black hole is determined analytically. Our results support the possible existence of stationary scalar field dark matter distributions surrounding rapidly rotating black holes.

Electron transport properties of stationary plasma clouds generated with hollow cathode discharges

The electron transport in plasma clouds generated by a hollow cathode electric discharge are investigated. The voltage current characteristic curves indicate that the emitted current depends on bias voltage and discharge current. The measurements of the spatial dependence of the electronic density, plasma potential and electronic temperature are also presented. The energy loss rate of a high energy group of electrons with the radial distance is also measured. These experimental results are compared with a nonisothermal transport model which reproduces the spatial dependence of plasma properties.

Altitude effect on the clearness index in the French alps

Simultaneous measurements of horizontal global solar irradiance were done over three years, at altitudes ranging from 200 m to 1,700 m in an industrial alpine valley, for studying the clearness index variations versus height. Estimated values of the Ångström coefficient suggested that the main cause of depletion of the clear sky clearness index k c at the lower levels was the scattering by the aerosols. For irradiances, a depletion term D = 1 − k c was empirically assumed to be a function of the altitude z, as simple as D = ( Mz + N) −1. A study carried out over 8,000 10-minute sequences of measurement, during clear sky periods, showed that the coefficient M was sensible to the season only, while N was mainly a function of the sun elevation h such as N = A( h − C) 0.5 + B; from 240 m to 1,100 m, k c was found increasing by about 12% for h = 30° and 7% for h = 60°. The yearly global horizontal irradiation, although including many cloudy sequences, appeared linearly related to ln( z), its relative increase between 200 m and 1,700 m rising 10%; whereas, for shorter periods, the monotony of the vertical profiles of the clearness index for irradiation was often significantly affected by local stationary clouds or seasonal mists.

二波長レーダーで観測される融解中の雪片の微物理過程

Microphysical processes in the melting layer were studied using two-wavelength radar observation.Dependence of microwave scattering by precipitation particles on radar wavelength was utilized applying the model calculations shown in Part I of Yokoyama and Tanaka (1984). The observation was performed from the end of June to the begining of July, 1979 (rainy season in Japan) using C-band (5.6cm) and X-band (3.2cm) radars. It is clearly found from the results of the observation that coalescence processes are predominant in the upperhalf region of the melting layer as was already expected by the model calculation in Part-I. How predominant the coalescence processes in the melting layer are depends on precipitation types, that is, the coalescence processes in the precipitation associated with stratiform and stationary clouds are more predominant than with cellular clouds. The effects of evaporation was also found when the atmosphere was dry around the melting layer. In the lowerhalf region of the melting layer, it was difficult to detect the microphysical processes when we use C- and X-hand radars.

Theoretical considerations of the warp and thickening

As a theoretical subject, the study of the bending of the gaseous planes of galaxies has not been extremely popular. It seems that this is due to an excellent and thorough paper on the subject, published by Hunter and Toomre in 1969. At that time there existed three (or four) rival theoretical mechanisms:(1)vertical oscillations of the galactic disk, considered first by Lynden-Bell (1965);(2)asymmetrical pressure on the disk due to intergalactic wind (Kahn and Woltjer 1959);(3)tidal influence of the Magellanic Clouds, from(a)the case of Stationary Clouds, and(b)the case of Clouds orbiting around the Galaxy (Elwert and Hablick 1965, Avner and King 1967).

On low fogs and stationary clouds

The object of the present paper is to point out the circumstances which influence the formation of low fogs, and to show what ana­logy exists between the causes that produce them and those that occasion certain forms of clouds, which may be considered as differ­ing from fogs only in position. Having been attached for several years to the naval party employed in the survey of the gulf and river of St. Lawrence, the author had ample opportunities of observing the phenomena in question. He concludes that the fogs described oc­cur chiefly when the air is nearly saturated with moisture, and when at the same time the temperature of the water on which they rest either exceeds that of the air, or is considerably below it. These fogs are generally very dense, often limiting the sphere of vision to a few fathoms; but seldom extend to any considerable height. They do not often cover the land to any distance from the shore; and the tops of the hills, close to the water’s edge, are clear, while the bases, or sides, are enveloped in the mist.