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We find an infinite sequence of axially symmetric multipole solutions of Einstein equations in space-time of rigidly moving dust along field lines of time translation Killing vector. The resulting line element is necessarily of the van-Stockum class. The corresponding space-times are smooth, apart from the centre, stationary, asymptotically flat, and, for… (More)

- Joanna Ja locha, Lukasz Bratek, Marek Kutschera
- 2008

An iterative method for reconstructing mass distribution in spiral galaxies using a thin disk approximation is developed. As an example, the method is applied to galaxy NGC 4736; its rotation curve does not allow one to employ a model with a massive spherical halo. We find a global mass distribution in this galaxy (without non-baryonic dark matter) that… (More)

- LUKASZ BRATEK
- 2002

The hedgehog Skyrme model on three-sphere admits very rich spectrum of solitonic solutions which can be encompassed by a strikingly simple scheme. The main result of this paper is the statement of the tripartite structure of solutions of the model and the discovery in what configurations these solutions appear. The model contains features of more… (More)

We study numerically self-trapped (polaron) states of quasiparticles (electrons, holes or excitons) in a deformable nanotube formed by a hexagonal lattice, wrapped into a cylinder (carbon-and boron nitride-type nanotube structures). We present a Hamiltonian for such a system taking into account an electron-phonon interaction, and determine conditions under… (More)

- Lukasz Bratek
- 2009

Breathing rotators are relativistic dynamical systems consisting of a single null vector associated with position and described by a relativistically invariant action. They extend a class of rotators recently considered by Staruszkiewicz in the context of rigid bodies of Hanson and Regge. Of great interest are fundamental dynamical systems, that is such,… (More)

- Lukasz Bratek, Marcin Kolonko
- ArXiv
- 2006

We present an algorithm of finding numerical solutions of pulsar equation. The problem of finding the solutions was reduced to finding expansion coefficients of the source term of the equation in a base of orthogonal functions defined on the unit interval by minimizing a multi-variable mismatch function defined on the light cylinder. We applied the… (More)

An algorithm of finding numerical solutions of pulsar equation is presented which is essentially different from the one used in the pioneering paper by Contopoulos, Kazanas & Fendt. The problem of finding the solutions was reduced to finding expansion coefficients of the source term in a base of orthogonal functions on the unit interval by minimizing a… (More)

- Joanna Ja locha, Lukasz Bratek, Marek Kutschera, Piotr Skindzier
- 2009

figures available on request (ArXiv compiler has problems with them) ABSTRACT A global disk model is applied to find mass distribution in spiral galaxies NGC 1365, NGC 6946, NGC 7793. The obtained B-band mass-to-luminosity ratio is lower than 4 for three galaxies. It is consistent with pure baryon matter composition with no need to invoke non-baryonic… (More)

We discuss different classes of van Stockum spacetimes which are stationary and axisymmetric spacetimes of dust rotating rigidly on trajectories of the time translation Killing vector. The flow has no Newtonian limit. Asymptotically flat solutions are not physically viable. As an example we construct a sequence of asymptoti-cally flat internal multipolar… (More)

- L Bratek
- 2005

It is shown how the appearance of the 1-skyrmion on the three-sphere of radius L can be understood quantitatively by analyzing spectrum of the Hessian at the identity solution. Previously, this analysis was done qualitatively by N. Manton 7 which used a conformal deformation of the identity solution. Analysis of critical appearance of solutions in the… (More)

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