Shadows and photon rings of binary black holes

In this paper we present the images of binary black holes using the Majumdar-Papapetrou multiblack hole solution, depending on the parameters of the problem: the mass of black holes, the distance between them, and the inclination of the observer. The images consists of a shadows and photon rings. We find that a photon ring structure appears between black holes. The trajectories of the photons are calculated

Thick fluid disks around binary black holes

A model of a thick fluid disk around a binary black hole is considered. A binary black hole is described by the Majumdar-Papapetrou solution. The hydrodynamic equations in this metric are written out. Exact analytical solutions are presented. Generalization to the case of a toroidal magnetic field is carried out

Ultra-hard fluid and scalar field in the Kerr-Newman metric

An analytic solution for the accretion of ultra-hard perfect fluid onto a moving Kerr-Newman black hole is found. This solution is a generalization of the previously known solution by Petrich, Shapiro and Teukolsky for a Kerr black hole. Our solution is not applicable for an extreme black hole due to violation of the test fluid approximation. We also present a stationary solution for a massless scalar field in the metric of a Kerr-Newman naked singularity.Comment: 9 pages, 3 figures, revtex4; v2: presentation improved, figures added, matches published versio

Billiards with polynomial mixing rates

While many dynamical systems of mechanical origin, in particular billiards, are strongly chaotic -- enjoy exponential mixing, the rates of mixing in many other models are slow (algebraic, or polynomial). The dynamics in the latter are intermittent between regular and chaotic, which makes them particularly interesting in physical studies. However, mathematical methods for the analysis of systems with slow mixing rates were developed just recently and are still difficult to apply to realistic models. Here we reduce those methods to a practical scheme that allows us to obtain a nearly optimal bound on mixing rates. We demonstrate how the method works by applying it to several classes of chaotic billiards with slow mixing as well as discuss a few examples where the method, in its present form, fails.Comment: 39pages, 11 figue

Adatom incorporation and step crossing at the edges of 2D nanoislands

Adatom incorporation into the ``faceted'' steps bordering the 2D nanoislands is analyzed. The step permeability and incorporation coefficients are derived for some typical growth situations. It is shown that the step consisting of equivalent straight segments can be permeable even in the case of fast egde migration if there exist factors delaying creation of new kinks. The step consisting of alternating rough and straight segments may be permeable if there is no adatom transport between neighboring segments through the corner diffusion.Comment: 3 pages, one figur

The wave function of a gravitating shell

We have calculated a discrete spectrum and found an exact analytical solution in the form of Meixner polynomials for the wave function of a thin gravitating shell in the Reissner-Nordstrom geometry. We show that there is no extreme state in the quantum spectrum of the gravitating shell, as in the case of extreme black hole.Comment: 7 pages, 1 figur