We study the behavior of orbits in a galactic dynamical model composed of an harmonic core and a strong bar potential. Numerical calculations suggest that low angular momentun orbits display chaotic motion. The area on the x-px phase plane covered by chaotic orbits increases as the angular velocity of the system increases or the strength of the harmonic term decreases. The S(c) spectrum is introduced and used to detect the island motion and study the evolution of the sticky regions. Comparison with previous work is also made revealing the leading role of the new spectrum.

The planetary system 55Cnc consists of four planets. Two of the planets, the companions b and c, seem to be in a 3:1 mean motion resonance and the corresponding dynamics is of special interest. First we study the stability of the system in the framework of the three body problem. We show that the system is located in the neighborhood of an asymmetric periodic orbit in phase space and the corresponding resonant angle variables librate. The asymmetry, which is obeyed by the motion, is essential for the long-term stability. If the system was in a symmetric configuration then the evolution would be chaotic. Additional numerical simulations are performed in order to show the effect of the rest planets in the stability of the overall planetary system.

It is suggested that we accept that antiparticles move backward in time, as proposed by Feynman. Then, I show that we have to attribute negative mass and energy to antiparticles. Applying this to the presence of virtual particle-antiparticle pairs in the vacuum, we see that the vacuum has to be considered as containing zero mass-energy, instead of a huge amount of it resulting from considering the antiparticles´ mass-energy being positive. The result is that the cosmological constant has to be taken strictly zero, rather than having a huge value, resulting from taking of the mass-energy content of the vacuum as huge. Then the dark-energy based model universe, presupposing a small but finite cosmological constant, has to be abandoned. The problem then is what it has to be replaced with in order for the observasional data to be explained. To this end, I propose for the Universe a new exact cosmological solution of Einstein´s field equations (with no cosmological term), found by the author, which describes an accelerating expansion of the Universe, and a double rotation of it at the same time, which gives the Universe the shape of an (accelerating expanding) hypertorus. This new metric explains, besides the accelerating expansion of the Universe and the correct age of it, the Ryle effect and the observed large-scale anisotropy of the CMB. It also explains the apparent rotation and the spiral structure of galaxies, which latter one was the motivation underlying the work towards the new metric at the first place. (References under Chaliasos in arXiv.org/find)

Cosmic strings might influence galaxy formation and create the observed large scale structures of the Universe. Most galaxies and clusters are believed to lie on sheets, which intersect in higher density filaments and surround lower density voids. This sort of structure has an explanation within the cosmic string scenarios. Thus, we discuss charged cosmic string solutions to the Einstein field equations with Kerr-NUT parameter, named as (l) and examine the infuence of this parameter on the strength of the electromagnetic field. We also study the perturbed MHD equations close and far away from the charged cosmic string and search for stability criteria.

The interstellar space is full of small corpuscles of various shapes, sizes and physicochemical properties. These cosmic drifters derive from a variety of sources. The accumulation of these particles in some particular regions of outer space is an important issue, since it may provide answers to various scientific questions, such as the formation of proto-nebulae, planetary rings, interstellar clouds etc. In this work we suggest a possible mechanism of the genesis of such phenomena by studying the distribution of equilibrium positions of small particles that travel in the neighborhood of a system consisting of three major bodies that are in syzygy. Two of these bodies have equal masses m and are located at equal distances from a third primary with a different mass m0=βm. We also consider that some or all these bodies are radiation sources with constant luminosity. Therefore, the particle is subjected not only to gravitational forces but to the radiation emitted from the primaries as well. For our investigation we adopt Radzievskii’s simplifying theory which is mainly based on Lebedev’s inverse square law. The particular problem is characterized by four parameters: the mass parameter , and the three radiation coefficients , and which express the ratio of the force due to radiation to the force due to gravitation. These coefficients depend both on the properties of the radiating body and on those of the individual particle. This means that for a given source with constant luminosity, the corresponding radiation coefficient b has a unique value that characterizes a particular particle. Since there are many particles that move in the neighborhood of the primaries and assuming that the gravitational force exceeds radiation, the b-coefficients may take any value between 0 and 1. In the gravitational case there are six equilibrium positions of the particle. Four of them are collinear, that is, they lie on the x-axis of syzygy of the primaries and the other two are triangular and lie on the perpendicular y-axis that passes through the center of mass of the system. When only the central body is a radiation source, the equilibrium positions are spread along the two coordinate axes forming a cross. In all the other cases, the triangular points are arranged in arcs centered either to the central primary or a peripheral one and the collinear points, particularly those that are close to the radiating primary, scatter on the x-axis on both sides of each primary. These distributions remain qualitatively the same when the mass parameter of the system changes. As a special case of our investigation we have studied the distribution of the equilibrium points in the photo-gravitational Copenhagen problem.

We compute models of rotating neutron stars, emphasizing on calculating the mass increase due to differential rotation induced by the radial pulsations of the model(s). A brief description of our numerical approach has as follows. First, the unperturbed Oppenheimer-Volkoff equations are solved for several polytropic and realistic equations of state. Then, uniform rotation is inserted into the models in accordance with the Hartle's perturbation method (see, e.g., Hartle 1967; Hartle and Thorne 1968). At this stage, corrections to mass and radius, owing to spherical and quadrupole deformations, are calculated. Third, the perturbative approach to the structure of the model(s) up to terms of third order in angular velocity (see, e.g., Benhar et al. 2005) is carried out; angular momentum, moment of inertia, rotational kinetic energy, and gravitational potential energy are some of the quantities corrected drastically by such third order approach. Finally, differential rotation driven by the radial pulsations of the model(s) and the corresponding increase in mass (see, e.g., Hartle 1975; Hartle and Munn 1975) are calculated. Such a mass increase is discussed within the framework of its connection with the corresponding pulsation energy of the model(s) (see, e.g., Meltzer and Thorne 1966). REFERENCES: Benhar, O., Ferrari, V., Gualtieri, L., and Marassi, S. 2005, Phys. Rev. D, 72, 044028. Hartle, J. B. 1967, Ap. J., 150, 1005. Hartle, J. B. 1975, Ap. J., 195, 203. Hartle, J. B., and Munn, M. W. 1975, Ap. J., 198, 467. Hartle, J. B., and Thorne, K. S. 1968, Ap. J., 153, 807. Meltzer, D. W., and Thorne, K. S. 1966, Ap. J., 145, 514.

We propose that cosmological magnetic fields generated in regions of finite spatial dimensions may manifest themselves in the global dynamics of the Universe as `dark energy'. We test our model in the context of spatially flat cosmological models by assuming that the Universe contains non-relativistic matter $\rho_m\propto \alpha^{-3}$, dark energy $\rho_{Q}\propto \alpha^{-3(1+w)}$, and an extra fluid with $\rho_{B} \propto \alpha^{n-3}$ that corresponds to the magnetic field. We place constraints on the main cosmological parameters of our model by combining the recent supernovae type Ia data and the differential ages of passively evolving galaxies. In particular, we find that the model which best reproduces the observational data when $\Omega_m=0.26$ is one with $\Omega_{B}\simeq 0.03$, $n\simeq 7.68$, $\Omega_{Q}\simeq 0.71$ and $w\simeq -0.8$.

We do a systematic search of parameter space by computing crust torsional and global Alfvén modes for various values of the harmonic index l and for various overtones, where we use an extended sample of models of compact stars, varying in mass, high-density equation of state and crust model. As a result, we find excellent agreement between our computed frequencies and observed frequencies in two SGRs.

We study the influence of magnetic fields on the axial gravitational waves emitted during the collapse of a homogeneous dust sphere. We found that while the energy emitted depends weakly on the initial matter perturbations it has strong dependence on the strength and the distribution of the magnetic field perturbations. The gravitational wave output of such a collapse can be up to an order of magnitude larger or smaller calling for detailed numerical 3D studies of collapsing magnetized configurations.

We study the effects of rotation on the torsional modes of oscillating relativistic stars with a solid crust. Earlier works in Newtonian theory provided estimates of the rotational corrections for the torsional modes and suggested that they should become CFS unstable, even for quite low rotation rates. In this work, we study the effect of rotation in the context of general relativity using elasticity theory and in the slow-rotation approximation. We find that the Newtonian picture does not change considerably. The inclusion of relativistic effects leads only to quantitative corrections. The degeneracy of modes for different values of m is removed, and modes with l=m are shifted towards zero frequencies and become secularly unstable at stellar rotational frequencies ~20-30 Hz.

We study numerically the scattering of planet-size bodies by a planetary system, which is modelled by a Jupiter-sized planet, revolving around a Sun-like star. The calculations are made in the framework of the planar general three-body problem, and in each case we use 350.000 initial conditions on the 2-D configuration space of the system (impact parameter vs. planet phase angle). The final possible states of the system are (a) flyby, (b) planet exchange, (c) capture and (d) disruption. We find that in parts of the configuration space the boundaries between regions leading to different outcomes are fractal and we discuss how the properties of these boundaries (in particular the uncertainty dimension) and the probability of a certain final state depend on the various parameters of the dynamical system (e.g. mass of the bodies, energy and momentum of the incoming planet).

We present numerical results concerning the distances of the large trans-Neptunian objects (TNOs) Eris, 2005 FY9, 2003 EL61, Sedna, Orcus, Quaoar, Varuna, and 2002 AW197, computed by the so-called "global polytropic model". This model (Geroyannis 1993 [P1]; Geroyannis and Valvi 1993 [P2]) is based on the assumption of hydrostatic equilibrium for the solar system and its structure is described by the well-known Lane-Emden differential equation. A polytropic sphere of particular polytropic index n and radius R1 represents the central component S1 (in our case, the Sun) of a resultant polytropic configuration, of which further components are the polytropic spherical shells S2, S3, ..., defined by the pairs of radii (R1,R2), (R2,R3), ..., respectively. R1, R2, R3, ..., are the roots of the real part Re(theta(R)) of the complex Lane-Emden function theta(R), defined in the so-called "complex-plane strategy" (Geroyannis 1988). In this method, the complex Lane-Emden differential equation is solved numerically in the complex plane. Each polytropic shell can be considered as an appropriate place for a "planet" to be "born" and "live". This scenario has been studied numerically for the case of the planets of the solar system (P1, P2). In the present paper, we extend our computations far beyond Neptune, in order to include in our study the TNOs named above. REFERENCES: Geroyannis, V. S. 1988, Ap. J., 327, 273. Geroyannis, V. S. 1993, Earth, Moon, and Planets, 61, 131 [P1]. Geroyannis, V. S., and Valvi, F. N. 1993, Earth, Moon, and Planets, 63, 15 [P2].

In this paper, we solve numerically in the complex plane all the differential equations involved in Hartle's perturbative scheme for rapidly rotating neutron stars. We first find that some significant quantities (as the unperturbed radius and mass) remain almost invariable with respect to several trial imaginary initial values (of central density and pressure) varying over an orders-of-magnitude range. We then compare our numerical results with corresponding results of several nonperturbative methods, emphasizing on quantities describing the geometry of rapidly rotating models; we find appreciable improvement of our results in comparison with those given by the "classical" Hartle's scheme.

We present two-dimensional, numerical simulations of relativistic accretion onto a Schwarzschild black hole, including a density gradient in the initial conditions of the flow. Varying flow velocities, sound speeds, adiabatic indices and density gradients, we find that not only the morphology but also the stability of the flow is strongly dependent on the above parameters. More specifically, we find significant differences regarding the onset of the so-called flip-flop instability (which is associated with the shock cone in the rear part of the accretor) with respect to previous Newtonian studies.

It is generally considered that the X-ray emission in AGN and Galactic Black Hole Candidates is produced by flares above the surface of a geometrically thin optically thick accretion disk, which extends down to the Innermost Stable Circular Orbit (ISCO) of the black hole. We consider the influence of the black hole geometry on the light curves of these flares. To this end we follow a large number of photon orbits emitted impulsively in a locally isotropic fashion, at any phase of the disk orbit and examine their arrival times at infinity by an observer near the plane of the disk. We find out that the presence of the black hole spin induces a certain delay in the photon arrivals, as prograde photon orbits reach the observer on shorter (on the average) times than the retrograde ones. We form a histogram of the differences in photon time arrivals and we find that it exhibits several well defined peaks depending on the flare position and the black hole spin separated by $\Delta t \simeq 30 M$, where M is the black hole mass. The peaks disappear as the spin parameter goes to zero, implying that one could in principle measure the value of the black hole spin with timing measurements of sufficiently high signal to noise ratio

The latest results from the WMAP satellite confirm the success of the Lambda CDM model, where approximately 75 % of the mass-energy density is in the form of Dark Energy, and matter, most of it in the form of Cold Dark Matter (CDM) making up the remaining 25 %. Neutrinos with masses on the eV scale or below will be a hot component of the dark matter and will free-stream out of overdensities and thus wipe out small-scale structures. This fact makes it possible to use observations of the clustering of matter in the universe to put upper bounds on the neutrino masses. Present cosmological neutrino mass limits make use of the suppression effect of the neutrino free-streaming at a fixed, given redshift. As our ability to map out the mass distribution at different epochs of the cosmic history improves, by doing, e.g., weak lensing tomography, we will gain sensitivity by in addition using the effect of massive neutrinos on the growth rate of density fluctuations. One key issue which then arises is possible degeneracies between neutrino masses and cosmological parameters. We study the degeneracies between neutrino mass and Dark Energy as they manifest themselves in cosmological observations.

General relativity marked the beginning of modern cosmology and it has been at the centre of many of the key developments in this field. In the present review, we discuss the general-relativistic dynamics and perturbations of the standard cosmological model, the Friedmann-Lemaitre universe, and how these can explain and predict the properties of the observable universe. Our aim is to provide an overview of the progress made in several major research areas, such as linear and non-linear cosmological perturbations and large-scale structure formation, in view of current and upcoming observations. We do this by using a single formalism throughout the review, the 1+3 covariant approach to cosmology, which allows for a uniform and balanced presentation of technical information and physical insight.

We examine the orbital evolution of the Giant planets (Jupiter, Saturn, Uranus and Neptune) towards their currently observed configuration. The planets underwent large-scale orbital migration, during the early formation stages of our Solar system, as a result of their interaction with (i) the proto-planetary gas disc (first ~3-5 My), and (ii) the remnant disk of planetesimals, leftover planet-core formation. The second migration phase has been modeled successfully (the so-called Nice model, Tsiganis et al 2005, Gomes et al 2005), the results showing a remarkable agreement with observations. However, linking the two migration phases together and finding the appropriate initial conditions for the planetary system is a challenging issue. Here we present new results of extensive numerical simulations of the two migration phases. We show that the natural outcome of gas-driven migration is a multiply resonant planetary configuration, similar to the well-known Laplace resonance of the Gallilean satellites. Only a limited number of quadruple resonances are possible, some of which remain stable for very long times, after the dispersal of the gas disc. The planets then undergo planetesimal-driven migration, following a path very similar to that described by the Nice model. Migration stops when the disc of planetesimals is scattered away (~100-200 My). The final planetary orbits are very similar to their currently observed ones, in terms of all three orbital parameters (semi-major axes, eccentricities, and mutual inclinations).

The excitation of cosmological perturbations in an anisotropic cosmological model, in the presence of a homogeneous magnetic field has been studied, using the ideal magnetohydrodynamic (MHD) equations. We have shown that fast-magnetosonic modes, propagating normal to the magnetic field are excited. At late times, the magnetic induction contrast $(\dl B / B)$ grows according to a power-law temporal dependence, resulting in the amplification of the ambient magnetic field. This process can be particularly favored by condensations formed within the plasma fluid.

Constancy of the effective potential which governs the temporal evolution of a gravitational wave (GW) in an expanding Universe, leads to a critical comoving wave-number $(k_c)$, associated with a low-frequency cut-off in the corresponding energy-density. As a consequence, GW modes with $k \leq k_c$ remain outside the horizon for every $t$ and reduce to metric perturbations of constant amplitude. This property is met in a radiation model {\em contaminated} by a small fraction of cosmic strings. It is known that, the cosmological evolution gradually results in the {\em scaling} of the cosmic-string network and the Universe enters in the radiation era. Once the Universe becomes radiation-dominated, metric perturbations of $k \leq k_c$ are re-introduced inside the horizon, which now expands faster than their physical wavelength. Within the Hubble sphere, the energy-density associated with these waves makes up a logarithmically increasing fraction of the Universe matter energy-density.