Quasinormal modes of a black hole with quintessence-like matter and a deficit solid angle: scalar and gravitational perturbations

In the previous paper (Li et al. in Phys. Lett. B 666:125–130, 2008), we show the solutions of Einstein equations with static spherically-symmetric quintessence-like matter surrounding a global monopole. Furthermore, this monopole become a black hole with quintessence-like matter and a deficit solid angle when it is swallowed by an ordinary black hole. We study its quasinormal modes by WKB method in this paper. The numerical results show that both the real part of the quasinormal frequencies and the imaginary part decrease as the state parameter w, for scalar and gravitational perturbations. And we also show variations of quasinormal frequencies of scalar and gravitational fields via different ε (deficit solid angel parameter) and different ρ ₀ (density of static spherically-symmetric quintessence-like matter at r=1), respectively.     

Interpretation of the solar-like pulsational behaviour of η Bootis

HR 5235, better known as η Bootis, is a bright and well-known star for which very accurate observations have recently enabled Kjeldsen et al. (2003) and Carrier, Bouchy, and Eggenberger (2003) not only to confirm the presence of solar-like oscillations, but also to identify the excitation in the oscillation spectrum of several p-mode frequencies with harmonic degrees l = 0 – 2. Here we show how such observational success, through the calculation and the investigation of theoretical structure models and the comparison of the observed oscillation spectra with the predicted p-mode frequencies of oscillations, permits one to draw conclusions about the actual evolutionary state of this star and on the physical properties of its internal structure. The computation of the structure models is based on the use of updated global parameters and includes overshooting from the convective core. In particular, we consider the effect on the stellar structure, and hence on the theoretical frequencies, of employing different equations of state and different formalisms to describe the convective energy transport.     

Radioactivity of the Earth and the Case for Potassium in the Earth’s Core

The radioactivity of the earth is an important parameter in understanding the dynamics of the planet and the evolution of the crust–mantle–core system but geochemical and geophysical approaches have had only a limited success in defining it. The opportunity of a direct estimate of the radioactivity of the earth by measurement of the geoneutrino flux takes on an added significance in this context. Such an independent new measurement will help resolve and/or clarify a number of questions about global scale processes in the earth and will help advance earth sciences.     

Theory of relaxation of pulsar angular velocity within the framework of the general theory of relativity

The dynamics of the rotation of a two-component system in a neutron star is considered within the framework of the general theory of relativity. Equations for the angular velocities of the normal and superfluid components are obtained in the W approximation. It is shown that the solutions of these equations can describe the relaxation of pulsar angular velocity after a glitch. Translated from Astrofizika, Vol. 42, No. 1, pp. 89–100, January–March, 1999.     

Quintessential inflation models with a nonminimally coupled scalar field

The evolution of a homogeneous, isotropic cosmological model driven by a nonminimally coupled scalar field is studied. The potential for the quintessential inflation model proposed by Peebles and Vilenkin is selected as a scalar potential. Possible scenarios for the cosmological dynamics are described in the conformal Einstein and Jordan representations. It is shown that, unlike in models with a minimal scalar field, here a class of solutions exists for which the scalar field is fixed at finite values during cosmological expansion. __________ Translated from Astrofizika, Vol. 49, No. 3, pp. 487–498 (August 2006).     

Born–Infeld type phantom model in the ω–ω′ plane

In this paper, we investigate the dynamics of Born–Infeld (B–I) phantom model in the ω–ω′ plane, which is defined by the equation of state parameter for the dark energy and its derivative with respect to N (the logarithm of the scale factor a). We find the scalar field equation of motion in ω–ω′ plane, and show mathematically the property of attractor solutions which correspond to ω _φ ∼−1, Ω _φ =1, which avoid the “Big rip” problem and meets the current observations well.      

Energy–Momentum In The Viscous Kasner-Type Universe In Teleparallel Gravity

Using the teleparallel gravity versions of the Einstein and Landau–Lifshitz’s energy and/or momentum complexes, I obtain the energy and momentum of the universe in viscous Kasner-type cosmological models. The energy and momentum components (due to matter plus field) are found to be zero and this agree with a previous work of Rosen and Johri et al., who investigated the problem of the energy in Friedmann–Robertson–Walker (FRW) universe. The result that the total energy and momentum components of the universe in these models is zero same as Bergmann–Thomson’s energy–momentum and props the viewpoint of Tryon. Rosen found that the energy of the FRW space–time is zero, which agrees with the studies of Tryon. PACs Numbers: 04.20.-q; 04.50.+h An erratum to this article is available at .     

Earth–Mars transfers with ballistic escape and low-thrust capture

In this paper novel Earth–Mars transfers are presented. These transfers exploit the natural dynamics of n-body models as well as the high specific impulse typical of low-thrust systems. The Moon-perturbed version of the Sun–Earth problem is introduced to design ballistic escape orbits performing lunar gravity assists. The ballistic capture is designed in the Sun–Mars system where special attainable sets are defined and used to handle the low-thrust control. The complete trajectory is optimized in the full n-body problem which takes into account planets’ orbital inclinations and eccentricities. Accurate, efficient solutions with reasonable flight times are presented and compared with known results.     

Higher dimensional dust collapse with a cosmological constant

The general solution of the Einstein equation for higher dimensional (HD) spherically symmetric collapse of inhomogeneous dust in presence of a cosmological term, i.e., exact interior solutions of the Einstein field equations is presented for the HD Tolman–Bondi metrics embedded in a de Sitter background. The solution is then matched to exterior HD Schwarzschild–de Sitter. A brief discussion on the causal structure singularities and horizons is provided. It turns out that the collapse proceed in the same way as in the Minkowski background, i.e., the strong curvature naked singularities form and that the higher dimensions seem to favor black holes rather than naked singularities.      

The statistics of the photometric accuracy based on MASS data and the evaluation of high-altitude wind

The effect of stellar scintillation on the accuracy of photometric measurements is analyzed. We obtain a convenient form of estimaton of this effect in the long exposure regime, when the turbulence shift produced by the wind is much larger than the aperture of the telescope. A simple method is proposed to determine index S ₃ introduced by Kenyon et al. (2006), directly from the measurements with the Multi Aperture Scintillation Sensor (MASS) without information on vertical profile of the wind. The statistics S ₃ resulting from our campaign of 2005–2007 at Maidanak observatory is presented. It is shown that these data can be used to estimate high-altitude winds at pressure level 70–100 mbar. Comparison with the wind speed retrieved from the NCEP/NCAR global models shows a good agreement. Some prospects for retrieval of the wind speed profile from the MASS measurements are outlined.     

Conformally invariant model of the early universe

A model of the early universe in the Einstein theory of gravitation, supplemented by a conformalty invariant version of the Weinberg—Salam model, is considered. The conformai symmetry principle leads to the need to eliminate the Higgs potential from the expression for gravitational action, using the Lagrangian density of the model of Weinberg—Salam electroweak interactions as the material source, and to incorporate the conformally invariant Penrose—Chernikov—Tagirov term. In the limit of flat space, we arrive at the a version of the Weinberg—Salam model without Higgs particle-like excitations. In the conformalty invariant model under consideration, Higgs fields are absorbed by the spatial metric, so one can assume that the masses of elementary particles originate at the time when the evolution of the universe begins. Translated from Astrofizika, Vol. 41, No. 3, pp. 459–471, July–September, 1998.     

Some results on the global dynamics of the regularized restricted three-body problem with dissipation

We perform an analysis of the dynamics of the circular, restricted, planar three-body problem under the effect of different kinds of dissipation (linear, Stokes and Poynting–Robertson drags). Since the problem is singular, we implement a regularization technique in the style of Levi–Civita. The effect of the dissipation is often to decrease the semi-major axis; as a consequence the minor body collides with one of the primaries. In general, it is quite difficult to find non-collision orbits using random initial conditions. However, by means of the computation of the Fast Lyapunov Indicators (FLI), we obtain a global view of the dynamics. Precisely, we detect the regions of the phase space potentially belonging to basins of attraction. This investigation provides information on the different regions of the phase space, showing both collision and non-collision trajectories. Moreover, we find periodic orbit attractors for the case of linear and Stokes drags, while in the case of the Poynting–Robertson effect no other attractors are found beside the primaries, unless a fourth body is added to counterbalance the dissipative effect.     

Polar Coronal Structures and the Global Magnetic Field Evolution Through the Cycle

We compare the shape and position of some plasma formations visible in the polar corona with the cyclic evolution of the global magnetic field. The first type of object is polar crown prominences. A two-fold decrease of the height of polar crown prominences was found during their poleward migration from the middle latitudes to the poles before a polar magnetic field reversal. The effect could be assigned to a decrease of the magnetic field scale. The second type of object is the polar plumes, ray like structures that follow magnetic field lines. Tangents to polar ray structures are usually crossed near some point, “a magnetic focus,” below the surface. The distance q between the focus and the center of the solar disk changes from the maximum value about 0.65 R _⊙ at solar minimum activity to the minimum value about 0.45 R _⊙ at solar maximum. At first glance this behaviour seems to be contrary to the dynamics of spherical harmonics of the global magnetic field throughout a cycle. We believe that the problem could be resolved if one takes into account not only scale changes in the global magnetic field but also the phase difference in the cyclic variations of large-scale and small-scale components of the global field.     

Optimal low-thrust transfers between libration point orbits

Over the past three decades, ballistic and impulsive trajectories between libration point orbits (LPOs) in the Sun–Earth–Moon system have been investigated to a large extent. It is known that coupling invariant manifolds of LPOs of two different circular restricted three-body problems (i.e., the Sun–Earth and the Earth–Moon systems) can lead to significant mass savings in specific transfers, such as from a low Earth orbit to the Moon’s vicinity. Previous investigations on this issue mainly considered the use of impulsive maneuvers along the trajectory. Here we investigate the dynamical effects of replacing impulsive ΔV’s with low-thrust trajectory arcs to connect LPOs using invariant manifold dynamics. Our investigation shows that the use of low-thrust propulsion in a particular phase of the transfer and the adoption of a more realistic Sun–Earth–Moon four-body model can provide better and more propellant-efficient solution. For this purpose, methods have been developed to compute the invariant tori and their manifolds in this dynamical model.     

The Influence of the Electron κ-Distribution in the Solar Corona on the Fe VIII – Fe XV Line Intensities

Changes in the excitation equilibrium of Feviii – Fe xv in the solar corona due to the electron non-thermal κ-distribution are studied. The shape of the distribution affects the electron excitation rate and thus the relative intensities of the spectral lines. Since the shape of the electron distribution function influences also the ionization equilibrium of Fe, both effects change the final intensities of the lines. Possibilities for diagnostics of the shape of the electron distribution in the solar corona are discussed. Synthetic spectrum of Fe for T = 1.58× 10⁶ K and n_e = 10⁸ cm⁻³ is shown together with the synthetic spectra computed with DEM for the quiet Sun.     

Semi-classical Gravitational Effects Around Global Monopoles in Lyra Geometry

W.A. Hiscock (1990, Class. Quantum Gravitation 7, L235) obtained the vacuum expectation value of the stress-energy tensor of an arbitrary collection of conformal massless free quantum fields (scalar, spinor and vectors) in the space-time of a static global monopole. With this stress-energy tensor, the semi-classical Einstein equations are solved retaining terms up to first order in ħ in Lyra geometry. This revised version was published online in July 2006 with corrections to the Cover Date.     

Conformal analogs of the Jordan-Brans-Dicke theory. I.

Recent cosmological observations of large-scale structures (red shift of type Ia supernovae) confirm that the universe is currently expanding at an accelerating rate and its dominant component is dark energy. This has stimulated the development of the theory of gravity and led to many alternative variants, including tensor-scalar ones. This paper deals with the role of conformal transformations in the Jordan-Brans-Dicke theory. Variants of intrinsic, conformally coupled, and Einstein representations are examined. In the Einstein representation an exact analytic solution for the standard cosmological model is obtained. It is expressed in terms of the relative energy contributions of ordinary matter Ω _m , the scalar field Ω _CK , and a term Ω_Λ related to the cosmological constant Λ . Information on the evolution of the universe for the case with a minimally coupled scalar field is given in the form of graphs.     

Astrophysically useful radiative transition parameters for?the?e1Π–X1Σ+ and 1Σ+–X1Σ+ systems of zirconium oxide

The zirconium oxide (ZrO) is well known for its astrophysical importance. The radiative transition parameters that include Franck-Condon (FC) factor, r-centroid, electronic transition moments, Einstein coefficient, band oscillator strengths, radiative life time and effective vibrational temperature have been estimated for e ¹Π–X ¹Σ⁺ and ¹Σ⁺–X ¹Σ⁺ band systems of ⁹⁰ZrO molecule for the experimentally known vibrational levels using RKR potential energy curves. A reliable numerical integration method has been used to solve the radial Schr?dinger equation for the vibrational wave functions of upper and lower electronic states based on the latest available spectroscopic data and known wavelengths. The estimated radiative transition parameters are tabulated. The effective vibrational temperatures of these band systems of ⁹⁰ZrO molecule are found to be below 4200 K. Hence, the radiative transition parameters help us to ascertain the presence of ⁹⁰ZrO molecule in the interstellar medium, S stars and sunspots.     

Chaotic quasi-collision trajectories in the 3-centre problem

We study a particular kind of chaotic dynamics for the planar 3-centre problem on small negative energy level sets. We know that chaotic motions exist, if we make the assumption that one of the centres is far away from the other two (see Bolotin and Negrini, J Differ Equ 190:539–558, 2003): this result has been obtained by the use of the Poincaré-Melnikov theory. Here we change the assumption on the third centre: we do not make any hypothesis on its position, and we obtain a perturbation of the 2-centre problem by assuming its intensity to be very small. Then, for a dense subset of possible positions of the perturbing centre in \mathbbR²{\mathbb{R}^2} , we prove the existence of uniformly hyperbolic invariant sets of periodic and chaotic almost collision orbits by the use of a general result of Bolotin and MacKay (Celest Mech Dyn Astron 77:49–75, 77:49–75, 2000; Celest Mech Dyn Astron 94(4):433–449, 2006). To apply it, we must preliminarily construct chains of collision arcs in a proper way. We succeed in doing that by the classical regularisation of the 2-centre problem and the use of the periodic orbits of the regularised problem passing through the third centre.