Why not a di-NUT? or Gravitational duality and rotating solutions

We study how gravitational duality acts on rotating solutions, using the Kerr-NUT black hole as an example. After properly reconsidering how to take into account both electric (i.e. mass-like) and magnetic (i.e. NUT-like) sources in the equations of general relativity, we propose a set of definitions for the dual Lorentz charges. We then show that the Kerr-NUT solution has non-trivial such charges. Further, we clarify in which respect Kerr's source can be seen as a mass M with a dipole of NUT charges.Comment: 20 pages. v2: minor clarifications in section 4, version to appear in PR

Redshift distribution of {\bf Ly-α\alpha} lines and metal systems

The observed redshift distribution of Ly-$\alpha$ lines and metal systems is examined in order to discriminate and to trace the evolution of structure elements observed in the galaxy distribution, at small redshifts, and to test the theoretical description of structure evolution. We show that the expected evolution of filamentary component of structure describes quite well the redshift distribution of metal systems and stronger Ly-$\alpha$ lines with $\log(N_{HI})\geq$14, at $z\leq$ 3. The redshift distribution of weaker Ly-$\alpha$ lines can be attributed to the population of poorer structure elements (Zel'dovich pancakes), which were formed at high redshifts from the invisible DM and non luminous baryonic matter, and at lower redshifts they mainly merged and dispersed.Comment: 13 pages, 5 figures, accepted in MNRA

Statistical characteristics of observed Ly-α\alpha forest and the shape of linear power spectrum

Properties of $\sim$ 6 000 Ly-$\alpha$ absorbers observed in 19 high resolution spectra of QSOs are investigated using the model of formation and evolution of DM structure elements based on the Zel'dovich theory. This model asserts that absorbers are formed in the course of both linear and nonlinear adiabatic or shock compression of dark matter (DM) and gaseous matter. It allows us to link the column density and overdensity of DM and gaseous components with the observed column density of neutral hydrogen, redshifts and Doppler parameters of absorbers and demonstrates that at high redshifts we observe a self similar period of structure evolution with the Gaussian initial perturbations. We show that the colder absorbers are associated with rapidly expanded regions of a galactic scale which represent large amplitude negative density perturbations. We extend and improve the method of measuring the power spectrum of initial perturbations proposed in Demia\'nski & Doroshkevich (2003b). Our method links the observed separations and the DM column density of absorbers with the correlation function of the initial velocity field. We recover the cold dark matter (CDM) like power spectrum at scales 10> D > 0.15Mpc/h with a precision of ~15%. However at scales $\sim 3 - 150 h^{-1}$kpc the measured and CDM--like spectra are different. This result suggests a possible complex inflation with generation of excess power at small scales.Comment: 21 pages, 7 figures, MNRAS submitte

A stationary vacuum solution dual to the Kerr solution

We present a stationary axially symmetric two parameter vacuum solution which could be considered as ``dual'' to the Kerr solution. It is obtained by removing the mass parameter from the function of the radial coordinate and introducing a dimensionless parameter in the function of the angle coordinate in the metric functions. It turns out that it is in fact the massless limit of the Kerr - NUT solution.Comment: Latex, 4 pages, minor modifications in title and discussion. Accepted in Mod. Phys. Lett.

Einstein-Born-Infeld on Taub-NUT Spacetime in 2k+2 Dimensions

We wish to construct solutions of Taub-NUT spacetime in Einstein-Born-Infeld gravity in even dimensions. Since Born-Infeld theory is a nonlinear electrodynamics theory, in leads to nonlinear differential equations. However a proper analytical solution was not obtain, we try to solve it numerically (by the Runge-Kotta method) with initial conditions coinciding with those of our previous work in Einstein-Maxwell gravity. We solve equations for 4, 6 and 8 dimensions and do data fitting by the least-squares method. For N=l=b=1, the metric turns to the NUT solution only in 8 dimensions, but in 4 and 6 dimensions the spacetime does not have any Nut solution.Comment: 8 pages, 5 figure

High redshift constraints on dark energy models and tension with the flat LambdaCDM model

So far large and different data sets revealed the accelerated expansion rate of the Universe, which is usually explained in terms of dark energy. The nature of dark energy is not yet known, and several models have been introduced: a non zero cosmological constant, a potential energy of some scalar field, effects related to the non homogeneous distribution of matter, or effects due to alternative theories of gravity. In [1, 2] a tension with the flat LambdaCDM model has been discovered using a high-redshift Hubble diagram of supernovae, quasars, and gamma-ray bursts. Here we use Union2 type Ia supernovae (SNIa) and Gamma Ray Bursts (GRB) Hubble diagram, and a set of direct measurements of the Hubble parameter to explore different dark energy models. We use the Chevallier-Polarski-Linder (CPL) parametrization of the dark energy equation of state (EOS), a minimally coupled quintessence scalar field, and, finally, we consider models with dark energy at early times (EDE). We perform a statistical analysis based on the Markov chain Monte Carlo (MCMC) method, and explore the probability distributions of the cosmological parameters for each of the competing models. We apply the Akaike Information Criterion (AIC) to compare these models: our analysis indicates that an evolving dark energy, described by a scalar field with exponential potential is favoured by observational data.Comment: 27 pages, 11 figures submitted to JCA

Secular interactions between inclined planets and a gaseous disk

In a planetary system, a secular particle resonance occurs at a location where the precession rate of a test particle (e.g. an asteroid) matches the frequency of one of the precessional modes of the planetary system. We investigate the secular interactions of a system of mutually inclined planets with a gaseous protostellar disk that may contain a secular nodal particle resonance. We determine the normal modes of some mutually inclined planet-disk systems. The planets and disk interact gravitationally, and the disk is internally subject to the effects of gas pressure, self-gravity, and turbulent viscosity. The behavior of the disk at a secular resonance is radically different from that of a particle, owing mainly to the effects of gas pressure. The resonance is typically broadened by gas pressure to the extent that global effects, including large-scale warps, dominate. The standard resonant torque formula is invalid in this regime. Secular interactions cause a decay of the inclination at a rate that depends on the disk properties, including its mass, turbulent viscosity, and sound speed. For a Jupiter-mass planet embedded within a minimum-mass solar nebula having typical parameters, dissipation within the disk is sufficient to stabilize the system against tilt growth caused by mean-motion resonances.Comment: 30 pages, 6 figures, to be published in The Astrophysical Journa