Some Bianchi type cosmological models in f(R) gravity

The modified theories of gravity, especially the f(R) gravity, have attracted much attention in the last decade. In this context, we study the exact vacuum solutions of Bianchi type I, III and Kantowski-Sachs spacetimes in the metric version of f(R) gravity. The field equations are solved by taking expansion scalar θ proportional to shear scalar σ which gives A=B ⁿ , where A and B are the metric coefficients. The physical behavior of the solutions has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated in each case.     

Cylindrically-symmetric matter distribution with a magnetic field in Einstein-Cartan Theory

In the first part the number of independent non-vanishing components of the 3-index torsion tensorQ _jk ⁱ is reduced from 24 (in general case) to 12 — for the case of cylindrical symmetry of the underlying manifold. In the second part of the paper we have obtained an exact solution of Einstein-Cartan-Maxwell equations representing a static cylinder of perfect fluid with an axial magnetic fieldH and non-zero spin densityK.     

Scalar field instability in multi-dimensional cosmology

The scalar field theory on the background of cosmological models with n(n ≥ 1) spaces of constant curvature is considered. We take the integrable case of Ricci flat internal spaces. The coupling between the scalar and the gravitational fields includes the minimal coupling as well as the conformal case. In the ground state of the scalar field we find the conditions for vacuum instability realized for most of the possible solutions to Einstein's equations if the coupling parameter takes appropriate values. For the excited states of the scalar field we show the induction of massive modes and discuss their properties.     

On static spherical symmetric solutions of the Bach-Einstein gravitational field equations

For field equations of 4th order, follwing from a Lagrangian “Ricci scalar plus Weyl scalar”, it is shown (using methods of non-standard analysis) that in a neighbourhood of Minkowski space there do not exist regular static spherically symmetric solutions. With that (besides the known local expansions about r = o nad r = ∞ resp.) for the first time a global statement on the existence of such solutions is given. Finally, this result will be discussed in connection with Einstein's particle programme.     

Exact cosmological solutions in the scalar-tensor theory with cosmological constant

Under the assumption of a power-law between the expansion factor of the Universe, and the scalar field (a ⁿ=c=const.) tensor theory with cosmological constant are reduced to quadrature. Several exact solutions are obtained, among them inflationary universes that have barotropic equation of state.     

Cosmological models in semi-classical and higher order gravitational theories

We have studied semiclassical models with a classical scalar field, givingexact solutions in the cases of a ⁴ and an exponentialself-interaction potential, in the last case we have also studied theinfluence of the vacuum polarization terms on the stability of the power-lawsolutions. We have also found cosmological exact solutions to the higherorder gravitational equations derived from a Lagrangian with a R ^k Rstructure, and investigated the stability of the de Sitter and Minkowskispace-time in the sixth order approximation of this theory.     

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.     

Geodesics around oscillatons made of exponential scalar field potential

Some of the spherically symmetric solutions to the Einstein–Klein–Gordon (EKG) equations can describe the astronomical soliton objects made of a real time-dependent scalar fields. The solutions are known as oscillatons which are non-singular satisfying the flatness conditions asymptotically with periodic (separated) time-dependency. In this paper, we investigate the geodesic motion around an oscillaton. The Spherically Symmetric Geometry allows the bound orbits in the plan \(\theta=\frac{\pi}{2}\) under a given initial conditions. The potential for the scalar field \(\varPhi=\varPhi(r,t)\), is an exponential function of the form \(V(\varPhi)=V_{0}\exp(\lambda\sqrt{k_{0}}\varPhi)\).     

The Einstein-Maxwell field equations,II

In order to arrive at more general results solving Einstein-Maxwell's equations our investigation is centered around an electromagnetic spin tensor, which must be chosen in such a way that conservation laws still hold. This notion of the combined tensor is of course closely linked with the unified field equations. We shall avoid in this way the problem of the form of the matter tensor and neglect non-linear gravitational terms in the Ricci tensor. Then, the field equations have as solutionsh _ij=h _ij ^(P) +h _ij ^(h) , whereh _ij ^(P) are particular solutions, which are obtained by direct calculations andh _ij ^(h) are solutions of h _ij ^(h) =0. The quantitiesh _ij ^(P) are purely electromagnetic in nature, whileh _ij ^(h) may represent purely gravitational terms. The results obtained complete the ones which have been published already in the preceeding paper (Dionysiou, 1980a; which will hereafter be referred to as Paper I).     

The plane symmetric vacuum solutions of modified field equations in metric f(R) gravity

The f(R) theories of gravity have been interested in recent years. A considerable amount of work has been devoted to the study of modified field equations with the assumption of constant Ricci scalar which may be zero or nonzero. In this paper, the exact vacuum solutions of plane symmetric spacetime are analyzed in f(R) theory of gravity. The modified field equations are studied not only for R=constant but also for general case R≠constant. In particular, we show that the Novotný-Horský and anti-de Sitter spacetimes are the exact solutions of the field equations with the non-zero constant Ricci scalar. Finally, the family of solutions with R≠constant is obtained explicitly which includes the Novotný-Horský, Kottler-Whittaker, Taub and conformally flat spacetimes.     

Domain walls with spherical symmetry

In this paper, we have evaluated solutions for Domain walls with sphericalsymmetry in four and five dimensional space time. Exact solutions ofEinstein equations coupled to scalar field with a potential V() are presented. Here scalar field depends both on radial and timecoordinates. Pressures perpendicular to the wall are taken to benon-zero. The solutions are obtained using functional separability ofmetric coefficients. Also we study the gravitational effects on testparticles.Pacs Nos: 04.20jb, 98.80 Bp     

Brans-Dicke Cosmology with non-vanishing Cosmological Constant and Non-Zero Curvature

A model of the universe based on Brans-Dicke theory with non-vanishing cosmological constant and non-zero curvature is studied. Equations (13) and (16) have been obtained by the assumption f(t) = φ(t)a ³ (t),which give the values of the scale factor, a(t) and scalar field, φ(t) in terms of the observable parameters. Also, for a particular case of matter dominated universe, Equation (20) is obtained which gives the relation between various parameters. This revised version was published online in July 2006 with corrections to the Cover Date.     

Planar solitonic filaments in solar physics

A new class of analytical solution of the coupled system of Da Rios-diffusion equation in magnetohydrodynamic (MHD) representing solitonic vortex filaments is obtained. One of the solutions is similar to the one found by Rogers and Schief describing a solitary wave propagating along a constant torsion vortex filament. Scalar magnetic diffusion equations are obtained by decomposing the magnetic filament along Frenet frame. The integral invariant of curvature is used to place limits on the diffused 100 eV plasma filament curvature. The resistivity of η=5×10^?5 ohm?cm—close to the stainless steel limit is used to approximate the Frenet curvature. From the scalar diffusion equations the vortex filaments are constrained to move along torsionless (planar) trajectories. Da Rios equations are coupled to diffusion equation to obtain a solitonic vortex diffused filaments. Due to bounds in time and length L we show that the model discussed is particularly useful in solar physics.     

Phase transition in Schwarzschild-de Sitter spacetime

Using a static massive spherically symmetric scalar field coupled to gravity in the Schwarzschild-de Sitter (SdS) background, first we consider some asymptotic solutions near horizon and their local equations of state (E.O.S.) on them. We show that near cosmological and event horizons our scalar field behaves as a dust. At the next step near two pure de Sitter or Schwarzschild horizons we obtain a coupling dependent pressure to energy density ratio. In the case of a minimally coupling this ratio is ?1 which springs to the mind thermodynamical behavior of dark energy. If having a negative pressure behavior near these horizons we concluded that the coupling constant must be ξ<¼. Therefore we derive a new constraint on the value of our coupling ξ. These two different behaviors of unique matter in the distinct regions of spacetime at present era can be interpreted as a phase transition from dark matter to dark energy in the cosmic scales and construct a unified scenario.     

The study of Gödel type solutions in f(R, ϕ) gravity

The aim of this paper is to study the Gödel type universe in modified f(R, ϕ) theory of gravity, where R stands for Ricci scalar and ϕ be the scalar potential. We investigate the modified field equations by using anisotropic and perfect fluid distributions. In particular, we consider two proposed models with some fixed values of parameters and investigate the exact solutions. The behaviour of energy conditions can be seen by a detailed graphical analysis. Furthermore, Tolman-Oppenheimer-Volkoff equation has been studied for both models in this theory. We have also discussed some exact solutions using perfect fluid. It is concluded that f(R, ϕ) theory of gravity support the phenomenon of cosmic expansion of the universe through Gödel type universe for both models.     

‘Quantized’ dimensions of sunspots and penumbra phenomenon

Several authors have studied solutions of Einstein's field equations for a conformally invariant scalar field with trace-free energy-momentum tensor for the Robertson-Walker models forK = 0, ± 1. The relationship of these solutions to a previously existing one by Som (1985) is discussed. TheK = 0 model derived by Innaiah and Reddy (1985) is shown to be a special case of the Bianchi type-I models due to Accioly, Vaidya and Som (1983a).     

Kasner-like,inflationary and steady-state solutions in multi-dimensional cosmology

Multi-dimensional cosmological models with n(n > 1) Ricci-flat spaces and a scalar field are discussed classically and with respect to canonical quantization. These models are integrable. Two classes of solutions are obtained. One class of solutions generalizes the Kasner solutions. For special additional conditions we find another solution describing extended inflation connected with a constant volume of the whole multidimensional space (steady-state).     

Einstein-Like Equations with Coupled-to-Matter Λ Term

We consider Einstein-like gravitational equations with Λ term proportional to the trace of the energy tensor. The possibility of Lagrangian formulation is shortly discussed. The theory is consistent with the present-day observations, both at the local and cosmological level. Horizon-free cosmological solutions are found and discussed. The initial condition S(0) = 0 (where S(t) is the expansion factor and t the cosmic time) requires hyperbolic space. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bianchi VI h with variable gravitational and cosmological constants

In order to study how the gravitational and the cosmological constants, G, Λ may vary, we consider two theoretical frameworks which are, a modification of the General Relativity and several scalar models (the standard, non-interacting and interacting models and their respective modifications to allow a G varying). We find exact self-similar solutions for the geometry Bianchi VI _h , (that is, the models: III, VI₀, and VI _h ,). Some physical and geometrical properties of the models are also discussed and we compare the obtained theoretical results with the current observational data. In the first of the theoretical models, we reach the conclusion that, from the structure of the field equations, the behaviour of Λ and G are related, but taking into account the observational data, we conclude that the Λ behaves as a positive decreasing time function while G is growing but in the long time regimen it tends to a constant value. In the scalar models, our solutions predict a “positive” dynamical cosmological constant in all the obtained solutions while the behaviour of G yields indeterminate, since its depends on a free parameter, G≈t ^2α , so it may be growing or decreasing as in the scalar-tensor theories.     

Collective plasma effects and the electron number problem in solar hard X-ray bursts

Due to the relatively high stream densities involved, collective interactions with the ambient plasma are likely to be important for the electrons producing solar hard X-ray bursts. In thick- and thin-target bremsstrahlung models the most relevant process is limitation of the invoked electron beams by ion sound wave generation in the neutralizing reverse current established in the atmosphere. For the thick target model it is shown that typical electron fluxes are near the maximum permitted by stability of the reverse current so that ion-sound wave generation may be the process which limits the electron injection rate. On the other hand the chromospheric reverse current is sufficient to supply the large total number of electrons which have to be accelerated in the corona. For the thin target the low density of the corona severely limits the possible reverse current so that the maximum upward flux of fast electrons is probably much too small to explain X-ray bursts but compatible with observations of interplanetary electrons.A distinct class of model postulates a small number of electrons confined by resonant scattering in a dense coronal slab surrounding a current sheet with continuous stochastic acceleration offsetting collisional losses. The energetic aspects of such a situation described by Hoyng (1975) are developed here by addition of equations describing the slab geometry in terms of electron diffusion by whistler scattering and of the collisional damping of the accelerating Langmuir waves. Solution of these equations results in values for the fieldB(70–350 G), densityn ₀(2–5 × 10¹² cm ^–3), slab dimensions (10¹⁸ km² × 0.3–3 km) and relative Langmuir energy density (10^–3 – 10^–2) required to produce the observed range of bursts. It is pointed out, however, that there may be no real gain in electron number requirements since the fast electrons in the emitting slab would be constantly swept out along with the frozen-in plasma as dissipation proceeds so that a large total number of electrons is still required. It could in fact be that just such a coronal region is the injection mechanism for the thick-target model.On leave from Department of Astronomy, University of Glasgow, Scotland.