Gravitational collapse in free fall of a slowly rotating star

The gravitational collapse of a slowly rotating star with small deviations from spherical symmetry is studied. The exterior metric is chosen to be the Kerr metric in synchronous coordinates discarding terms of order (a/r)². Interior geometry is constructed by adding an off-diagonal term in first order ofa to the exact solution of the non-rotating case. This term is determined in part by requiring the validity of the junction conditions at the star's surface and by demanding that the angular momentum of the source is equal toM A, in agreement with the value measured by a distant observer. The resulting stress-energy tensor describes a homogeneous, pressureless, ideal fluid which rotates nonuniformly relative to the synchronous frame which is no longer comoving the stellar matter.     

Stress-Energy Density Tensor of Isotropic Homogeneous Universe

The relation between timelike and spacelike components of the stress-energy density tensor is obtained from EINSTEIN equations in ROBERTSON -WALKER metrics. The timelike component of the stress-energy density tensor is developed as a power series of cosmological scaling radius. FRIEDMANN cosmology is recognized as a part of a more general cosmology.     

Hawking’s radiation in non-stationary rotating de Sitter background

Hawking’s radiation effect of Klein-Gordon scalar field, Dirac particles and Maxwell’s electromagnetic field in the non-stationary rotating de Sitter cosmological space-time is investigated by using a method of generalized tortoise co-ordinates transformation. The locations and the temperatures of the cosmological horizons of the non-stationary rotating de Sitter model are derived. It is found that the locations and the temperatures of the rotating cosmological model depend not only on the time but also on the angle. The stress-energy regularization techniques are applied to the two dimensional analog of the de Sitter metrics and the calculated stress-energy tensor contains the thermal radiation effect.     

Singular points of the polarization tensor

The problem to compute the magnetic field above the chromosphere using data of the vector = B _t/Bt that gives the projected field direction can be solved with different approximations. The field of direction vectors is, however, not the only field accessible to observations. The Stokes parameters, which are components of the radiation tensor, can be measured at each point of the image plane. The directions of the eigenvectors of the radiation tensor define two mutually orthogonal systems of integral curves in the image plane. These families of curves have singular points, which are generally of different type than those of the vector field. When the morphology of H chromospheric fibrils are used to infer the topology of the magnetic field, a similar problem is met, suggesting that singular points should also be present there.     

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).     

Irreversible Matter Creation in Inflationary Cosmology

Irreversible matter creation is investigated in a two-component (scalar field and ordinary matter) cosmological fluid in a homogeneous spatially flat and isotropic Friedmann-Robertson-Walker (FRW) inflationary Universe during its reheating era. The thermodynamics of open systems as applied together with the gravitational field equations to the two-component cosmological fluid leads to a generalisation of the elementary reheating theory in which the decay (creation) pressures are explicitly considered as parts of the fluid stress-energy tensor. Particular models describing coherently oscillating scalar waves and leading to a high particle production at the beginning of the oscillatory period are considered too. This revised version was published online in July 2006 with corrections to the Cover Date.     

Axially Symmetric String Cosmological Model In Brans-Dicke Theory of Gravitation

By adopting the co-moving coordinate system, an exact axially symmetric cosmological model with string dust cloud source is obtained in the framework of Brans-Dicke [Phys. Rev. 124, 925, (1961) Scalar – tensor theory of gravitation. Some physical and kinematical properties of the model are also discussed.     

Reconstruction of f(R,T) gravity in anisotropic cosmological models of accelerating universe

In this paper, we search the existence of Bianchi type I cosmological model in f(R,T) gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the trace of the stress-energy tensor T. We obtain the gravitational field equations in the metric formalism, and reconstruct the corresponding f(R,T) functions. Attention is attached to the special case, f(R,T)=f ₁(R)+f ₂(T) and two examples are assumed for this model. In the first example, we consider the unification of matter dominated and accelerated phases with f(R) gravity in anisotropic universe, and in the second instance, model of f(R,T) gravity with transition of matter dominated phase to the acceleration phase is obtained. In both cases, f(R,T) is proportional to a power of R with exponents depending on the input parameters.     

An inhomogeneous stiff fluid universe with electromagnetic field in general relativity

An inhomogeneous cylindrically symmetric cosmological model for stiff perfect fluid distribution with electromagnetic field is obtained.F ₁₂ is the non-vanishing component of electromagnetic field tensor. The metric potentials are functions ofx andt both. The behaviour of the electromagnetic field tensor together with geometrical and physical aspects of the model are also examined.     

The stress-energy tensor and the deflection of light in 6-dimensional general relativity

We find the stress-energy tensor of a perfect fluid in the 6-dimensional spacetime proposed by Cole. Using the weak-field Newtonian approximation of general relativity gives a constant of proportionality in Einstein's field equations that differs by a factor of 4/6 from the usual one and shows that Cole's extension of the Schwarzschild metric to 6 dimensions is not valid for a gravitating mass of ordinary matter. A subsequent evaluation of the deflection of starlight for the 6-d spacetime gives a result that is 4/6 of the 4-d result. We conclude that if spacetime is 6-dimensional, one must find a different way to deal with gravity.     

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.     

Application of the sine-Poisson equation in solar magnetostatics

Solutions of the sine-Poisson equation are used to construct a class of isothermal magnetostatic atmospheres, with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model j is directed along the x-axis, where x is the horizontal ignorable coordinate. The current j varies as the sine of the magnetostatic potential and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. We investigate in detail solutions for the magnetostatic potential A corresponding to the one-soliton, two soliton, and breather solutions of the sine-Gordon equation. Depending on the values of the free parameters in the soliton solutions, horizontally, periodic magnetostatic structures are obtained possessing either (a) a single X-type neutral point, (b) multiple neutral X-points, or (c) solutions without X-points. The solution cases (b) and (c) contain two families of intersecting current sheets, in which the line of intersection forms flux concentration points (or singularities) for the magnetic field. The solutions illustrate the contribution of the anisotropic J × B force (B, magnetic field induction), the gravitational force, and the gas pressure gradient to the force balance.     

Black Hole Solutions in Braneworlds with Induced Gravity

An analysis of a spherically symmetric braneworld configuration is performed when the intrinsic curvature scalar is included in the bulk action. In the case when the electric part of the Weyl tensor is zero, all the exterior solutions are found; one of them is of the Schwarzschild-(A)dS ₄ form, which is matched to a modified Oppenheimer-Volkoff interior solution. In the case when the electric part of the Weyl tensor is non zero, the exterior Schwarzschild-(A)dS ₄ black hole solution is modified receiving corrections from the non-local bulk effects. A non-universal gravitational constant arises, depending on the density of the considered object and the Newton's law is modified for small and large distances; however, the conventional limits are easily obtained. This revised version was published online in July 2006 with corrections to the Cover Date.     

The conformal potential of the stationary axisymmetric vacuum

In a stationary axisymmetric vacuum gravitational field, the conformal structure of the 3-space is determined by the symmetric, trace free and divergence-less tensor Y_ir. Using the Killing vector Kⁱ of the axisymmetry, the conformal potential U can be defined by U,_i = _εijkKjY^krK_r. Conversely, the tensor Y_ik is given algebraically in terms of the gradient U,_i of the conformal potential. An attempt is made here to re-formulate the field equations R_λμ = 0 in terms of the conformal potential. Introducing the Ernst potential as a complex coordinate, the cylindrical radius can be eliminated from the field equations.     

Do Long-Lived Features Really Exist in the Solar Photosphere? II. Contrast of Time-Averaged Granulation Images

The decrease in the rms contrast of time-averaged images with the averaging time is compared between four data sets: (1) a series of solar granulation images recorded at La Palma in 1993, (2) a series of artificial granulation images obtained in numerical simulations by Rieutord et al. (Nuovo Cimento 25, 523, 2002), (3) a similar series computed by Steffen and his colleagues (see Wedemeyer et al. in Astron. Astrophys. 44, 1121, 2004), (4) a random field with some parameters typical of the granulation, constructed by Rast (Astron. Astrophys. 392, L13, 2002). In addition, (5) a sequence of images was obtained from real granulation images by using a temporal and spatial shuffling procedure, and the contrast of the average of n images from this sequence as a function of n is analysed. The series (1) of real granulation images exhibits a considerably slower contrast decrease than do both the series (3) of simulated granulation images and the series (4) of random fields. Starting from some relatively short averaging times t, the behaviour of the contrast in series (3) and (4) resembles the t ^−1/2 statistical law, whereas the shuffled series (5) obeys the n ^−1/2 law from n=2 on. Series (2) demonstrates a peculiarly slow decline of contrast, which could be attributed to particular properties of the boundary conditions used in the simulations. Comparisons between the analysed contrast-variation laws indicate quite definitely that the brightness field of solar granulation contains a long-lived component, which could be associated with locally persistent dark intergranular holes and/or with the presence of quasi-regular structures. The suggestion that the random field (4) successfully reproduces the contrast-variation law for the real granulation (Rast in Astron. Astrophys. 392, L13, 2002) can be dismissed.     

Energization of plasma in a weak magnetic field and structure of the geomagnetic tail

A two-fluid plasma is described as a single continuum characterised by the generalised tensor of mechanical pressure and generalised vector of flow of mechanical energy. Plasma energization due to the transfer of mechanical energy inside the plasma body is emphasised and the energization of plasma by conversion of the electromagnetic energy into the mechanical energy is discussed. Two kinds of conversion associated with the convection electric field –(1/c)V×B and with the deviationE ^* of the total electric field from –(1/c)V×B are distinguished. TheV×B-field is related to the work done upon the plasma, while theE ^*-field is related to the plasma heating.Plasma motions with scale length larger than the Debye distance, taking place in the central part of the Earth-plasma sheet, are considered. The change of energy of any element of plasma is due mainly to the transfer of mechanical energy across the element's boundary; the EM-field is not strong enough to make a significant contribution. The work done by the internal loads is the main source of mechanical energy in the configurations in which the physical quantities do not vary along the current lines. The rates of change of the kinetic and internal energies are comparable. The transfer of mechanical energy is the principal source of the kinetic energy also in the general case when the physical quantities vary along the current lines. Conversion of the EM energy into mechanical energy is the main source of the internal energy in this case. In the tail plasma located outside the central part of the plasma sheet, conversion of the EM-energy into mechanical energy, which is due to the work done by the EM-force, takes place. The tail plasma is likely to undergo a two-phase energization process: first, it is accelerated and later, when it approaches the neutral sheet, it is heated.     

Perfect Fluid Lrs Bianchi I With Time Varying Constants

It is investigated the behaviour of the “constants” G, c and Λ in the framework of a perfect fluid LRS Bianchi I cosmological model. It has been taken into account the effects of a c-variable into the curvature tensor. Two exact cosmological solutions are investigated, arriving t the conclusion that if q < 0 (deceleration parameter) then G, c are growing functions on time t while Λ is a negative decreasing function on time.     

Unrestricted second-order tensor virial equations for linear oscillations of magnetic configurations

This paper deals with the second-order tensor virial equations for the linear oscillations of a gaseous mass in the presence of a magnetic field. It is shown that the commonly used linearized versions of the tensor virial equations are restricted integral equations that incorporate the linearized equation of motion but not the boundary condition. These restricted equations only allow trial functions that fulfil the boundary condition and are of limited practical value.The unrestricted variational principle for the linear oscillations of a magnetic configuration is used to derive a more general formulation of the second-order tensor virial equations so that the linear trial function _i =X _ij x _j can be used to study the oscillations of a configuration with a magnetic field that extends in the exterior vacuum. The unrestricted virial equations have been applied to Ferraro's model and approximate results for the eigenfrequencies and eigenfunctions have been obtained for nine oscillation modes.     

Compactification and cosmic string phenomenology

A U(1) model of gravitational, Higgs and, gauge fields is analysed. Two phases of the system are considered. In the case with broken symmetry we have the Nielsen-Olesen configuration. In the symmetric phase we find a space-time metric S² × E₁². This appears in full analogy to the Freund-Rubin compactification due to an antisymmeric tensor field. The connection of these structures with cosmic string phenomenology is analysed.     

Geometrie der Raum-Zeit der Maßbestimmung von KOTTLER,WEYL und TREFFTZ

The space-time manifold with the metric tensor of KOTTLER , WEYL and TREFFTZ (KWT) is analytically extended for all the three ranges 2m/a ⩽ 2/3^3/2 and the transformations into Kruskal-coordinates are given. The conformal infinity is represented by Penrose-diagrams. Finally embeddings in three-space are shown of surfaces with KWT-metric in cylindrical and spherical coordinates.