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

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

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

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

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.

Space-time symmetry restoration in cosmological models with Kalb--Ramond and scalar fields

We study symmetry of space-time in presence of a minimally coupled scalar field interacting with a Kalb--Ramond tensor fields in a homogeneous but initially anisotropic universe. The analysis is performed for the two relevant cases of a pure cosmological constant and a minimal quadratic, renormalizable, interaction term. In both cases, due to expansion, a complete spatial symmetry restoration is dynamically obtained.Comment: Latex, 7 pages, 3 eps figure

Quantum Oscillations Can Prevent the Big Bang Singularity in an Einstein-Dirac Cosmology

We consider a spatially homogeneous and isotropic system of Dirac particles coupled to classical gravity. The dust and radiation dominated closed Friedmann-Robertson-Walker space-times are recovered as limiting cases. We find a mechanism where quantum oscillations of the Dirac wave functions can prevent the formation of the big bang or big crunch singularity. Thus before the big crunch, the collapse of the universe is stopped by quantum effects and reversed to an expansion, so that the universe opens up entering a new era of classical behavior. Numerical examples of such space-times are given, and the dependence on various parameters is discussed. Generically, one has a collapse after a finite number of cycles. By fine-tuning the parameters we construct an example of a space-time which is time-periodic, thus running through an infinite number of contraction and expansion cycles.Comment: 8 pages, LaTeX, 4 figures, statement on energy conditions correcte

Are We Seeing Magnetic Axis Reorientation in the Crab and Vela Pulsars?

Variation in the angle $\alpha$ between a pulsar's rotational and magnetic axes would change the torque and spin-down rate. We show that sudden increases in $\alpha$, coincident with glitches, could be responsible for the persistent increases in spin-down rate that follow glitches in the Crab pulsar. Moreover, changes in $\alpha$ at a rate similar to that inferred for the Crab pulsar account naturally for the very low braking index of the Vela pulsar. If $\alpha$ increases with time, all pulsar ages obtained from the conventional braking model are underestimates. Decoupling of the neutron star liquid interior from the external torque cannot account for Vela's low braking index. Variations in the Crab's pulse profile due to changes in $\alpha$ might be measurable.Comment: 14 pages and one figure, Latex, uses aasms4.sty. Accepted to ApJ Letter

The most general axially symmetric electrovac spacetime adimitting separable equations of motion

We obtain the most general solution of the Einstein electro - vacuum equation for the stationary axially symmetric spacetime in which the Hamilton-Jacobi and Klein - Gordon equations are separable. The most remarkable feature of the solution is its invariance under the duality transformation involving mass and NUT parameter, and the radial and angle coordinates. It is the general solution for a rotating (gravitational dyon) particle which is endowed with both gravoelectric and gravomagnetic charges, and there exists a duality transformation from one to the other. It also happens to be a transform of the Kerr - NUT solution. Like the Kerr family, it is also possible to make this solution radiating which asymptotically conforms to the Vaidya null radiation.Comment: 9 pages, RevTex, Accepted by Class. Quantum Grav. Title, Abstract and some expressions have been modified, typos corrected. The solution and main result remain unaltere