Weighted Radon transforms for which the Chang approximate inversion formula is precise

We describe all weighted Radon transforms on the plane for which the Chang approximate inversion formula is precise. Some subsequent results, including the Cormack type inversion for these transforms, are also given

Hydrodynamics of primordial black hole formation

The hydrodynamic picture of the formation of primordial black holes (PBH) at the early stages of expansion of the Universe is considered. It is assumed that close to singularity, expansion occurs in a quasi-isotropic way. Using an EVM, a spherically symmetrical nonlinear problem of the evolution of primary strong deviation from the Fridman solution was solved. What these deviations must be, so that the formation of PBH occurred was clarified. Attention was devoted to the role of pressure gradients. It is pointed out that at the moment of formation of PBH, only a small part of matter enters into it, primarily the component of perturbation. It is also pointed out that at this moment, the mass of PBH essentially is smaller than the mass considered within the cosmic horizon. The possibility of changing the mass of the PBH as a result of accretion is analyzed

On the structure of line-driven winds near black holes

A general physical mechanism of the formation of line-driven winds at the vicinity of strong gravitational field sources is investigated in the frame of General Relativity. We argue that gravitational redshifting should be taken into account to model such outflows. The generalization of the Sobolev approximation in the frame of General Relativity is presented. We consider all processes in the metric of a nonrotating (Schwarzschild) black hole. The radiation force that is due to absorbtion of the radiation flux in lines is derived. It is demonstrated that if gravitational redshifting is taken into account, the radiation force becomes a function of the local velocity gradient (as in the standard line-driven wind theory) and the gradient of $g_{00}$. We derive a general relativistic equation of motion describing such flow. A solution of the equation of motion is obtained and confronted with that obtained from the Castor, Abbott & Klein (CAK) theory. It is shown that the proposed mechanism could have an important contribution to the formation of line-driven outflows from compact objects.Comment: 20 pages, submitted to Ap

Homogeneous singularities inside collapsing wormholes

We analyze analytically and numerically the origin of the singularity in the course of the collapse of a wormhole with the exotic scalar field Psi with negative energy density, and with this field Psi together with the ordered magnetic field H. We do this under the simplifying assumptions of the spherical symmetry and that in the vicinity of the singularity the solution of the Einstein equations depends only on one coordinate (the homogeneous approximation). In the framework of these assumptions we found the principal difference between the case of the collapse of the ordinary scalar field Phi with the positive energy density together with an ordered magnetic field H and the collapse of the exotic scalar field Psi together with the magnetic field H. The later case is important for the possible astrophysical manifestation of the wormholes.Comment: 10 pages, 5 figures each of which has a),b),c),and d) sub-figures. To be published in "Physical review. D, Particles, fields, gravitation, and cosmology

Penning traps as a versatile tool for precise experiments in fundamental physics

This review article describes the trapping of charged particles. The main principles of electromagnetic confinement of various species from elementary particles to heavy atoms are briefly described. The preparation and manipulation with trapped single particles, as well as methods of frequency measurements, providing unprecedented precision, are discussed. Unique applications of Penning traps in fundamental physics are presented. Ultra-precise trap-measurements of masses and magnetic moments of elementary particles (electrons, positrons, protons and antiprotons) confirm CPT-conservation, and allow accurate determination of the fine-structure constant alpha and other fundamental constants. This together with the information on the unitarity of the quark-mixing matrix, derived from the trap-measurements of atomic masses, serves for assessment of the Standard Model of the physics world. Direct mass measurements of nuclides targeted to some advanced problems of astrophysics and nuclear physics are also presented

Chirally Symmetric Phase of Supersymmetric Gluodynamics

We argue that supersymmetric gluodynamics (theory of gluons and gluinos) has a condensate-free phase. Unlike the standard phase, the discrete axial symmetry of the Lagrangian is unbroken in this phase, and the gluino condensate does not develop. Extra unconventional vacua are supersymmetric and are characterized by the presence of (bosonic and fermionic) massless bound states. A set of arguments in favor of the conjecture includes: (i) analysis of the effective Lagrangian of the Veneziano-Yankielowicz type which we amend to properly incorporate all symmetries of the model; (ii) consideration of an unsolved problem with the Witten index; (iii) interpretation of a mismatch between the strong-coupling and weak coupling instanton calculations of the gluino condensate detected previously. Impact on Seiberg's results is briefly discussed.Comment: Minor typos corrected; final version to appear in Phys. Rev.

The structure of the exact effective action and the quark confinement in MSSM QCD

An expression for the exact (nonperturbative) effective action of $N$=1 supersymmetric gauge theories is proposed, supposing, that all particles except for the gauge bosons are massive. Analysis of its form shows, that instanton effects in the supersymmetric theories can lead to the quark confinement. The typical scale of confinement in MSSM QCD, calculated from the first principles, is in agreement with the experimental data. The proposed explanation is quite different from the dual Higgs mechanism.Comment: Final version to appear in Sov.J.Nucl.Phys. Some insignificant errors and misprints are correcte

On Mass Spectrum in SQCD, and Problems with the Seiberg Duality. Equal quark masses

The dynamical scenario is considered for N=1 SQCD, with N_c colors and N_c<N_F<3N_c flavors with small but nonzero current quark masses m_Q\neq 0, in which quarks form the diquark-condensate phase. This means that colorless chiral quark pairs condense coherently in the vacuum, \neq 0, while quarks alone don't condense, ==0, so that the color is confined. Such condensation of quarks results in formation of dynamical constituent masses \mu_C \gg m_Q of quarks and appearance of light "pions" (similarly to QCD). The mass spectrum of SQCD in this phase is described and comparison with the Seiberg dual description is performed. It is shown that the direct and dual theories are different (except, possibly, for the perturbative strictly superconformal regime).Comment: 31 pages; text improved; corrections in sections 5,8; appendix added about 't Hooft triangle

London's limit for the lattice superconductor

A stability problem for the current state of the strong coupling superconductor has been considered within the lattice Ginzburg-Landau model. The critical current problem for a thin superconductor film is solved within the London limit taking into account the crystal lattice symmetry. The current dependence on the order parameter modulus is computed for the superconductor film for various coupling parameter magnitudes. The field penetration problem is shown to be described in this case by the one-dimensional sine-Gordon equation. The field distribution around the vortex is described at the same time by the two-dimensional elliptic sine-Gordon equation.Comment: 7 pages, 3 figures, Revtex4, mostly technical correction; extended abstrac

Classification of singular points in polarization field of CMB and eigenvectors of Stokes matrix

Analysis of the singularities of the polarization field of CMB, where polarization is equal to zero, is presented. It is found that the classification of the singular points differs from the usual three types known in the ordinary differential equations. The new statistical properties of polarization field are discussed, and new methods to detect the presence of primordial tensor perturbations are indicated.Comment: 7 pages, 1 figure