Circular radiation by a monopole around neutron stars

Radiation by a monopole which revolves round a neutron star is investigated in detail. Using radiant probabilityW _p ^t (k), we solve the radiant kinetic equation and proliferative equation of a monopole having the distribution functionf _p, and obtain the solution of wave numberN _k ^t (r) and distribution functionf _p. From these solutions, we know when the monopole moves round the neutron star; the exponential radiation is yielded with change of the motive orbit radiusr. As radiusr increases, the radiation appears as a saturated effect.     

Global Monopole and C-Field

It is well known that a C-field, generated by a certain source equation leads to interesting changes in the cosmological solutions of Einstein's equations. It is argued that different types of topological objects may have been created by the vacuum phase transitions in the early universe. In the cosmological arena, the defects have been put forward as a possible mechanism for structure formation. A global monopole is a heavy object formed in the phase transition of a system composed of a self coupling scalar field triplet φ^a whose original global 0(3) symmetry is spontaneously broken to U(1). In this article, we find a special solution for the space-time of a global monopole in presence of C-field. It is shown that the nature of the solution remains the same as in general relativity case i.e. monopole exerts no gravitational force on the matter surrounding it but space around it has a deficit solid angle. Pacs Nos: 98.80cq, 04.20jb, 04.50     

Quantum Vacuum Effects in the Gravitational Field of a Global Monopole

A study is made of the vacuum expectation values for the energy-momentum tensor of a massive scalar field that satisfy a Robin mixed boundary condition on a spherical surface with a background gravitational field from a D+1-dimensional global monopole. Expressions are derived for the Wightman function, vacuum expectation of the square of the field, vacuum energy density, and the radial and azimuthal pressures inside the spherical surface. The regularization procedure involves using the generalized Abel-Plana formula for series in terms of the zeroes of cylindrical functions. This formula makes it possible to separate the part owing to the gravitational field of a global monopole without boundaries from the vacuum expectation and to represent the parts induced by the boundary in the form of exponentially converging integrals which are especially convenient for numerical calculations. The asymptotic behavior of the vacuum averages is studied at the center of the sphere and near its surface. It is shown that for small values of the parameter describing the solid-angle deficit in the geometry of a global monopole, the vacuum stresses induced by the boundary are highly anisotropic.     

Cosmological models with the variable gravitational and cosmological constants

Cosmology with the gravitational and cosmological constants generalized as coupling scalars in Einsteins theory is considered. A general method of solving the field equations is given. Exact solution for Zeldovich fluid satisfying G=G ₀(R/R ₀) ⁿ is given.     

Some new exact solutions with finite central parameters and?uniform radial motion of sound

We present three new categories of exact and spherically symmetric Solutions with finite central parameters of the general relativistic field equations. Two well behaved solutions in curvature coordinates first category are being studied extensively. These solutions describe perfect fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing for these solutions. Keeping in view of well behaved nature of these solutions, one of the solution (I₁) is studied extensively. The solution (I₁) gives us wide range of Schwarzschild parameter u (0.138≤u≤0.263), for which the solution is well behaved hence, suitable for modeling of Neutron star. For this solution the mass of Neutron star is maximized with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. Corresponding to u=0.263, the maximum mass of Neutron star comes out to be 3.369 M _Θ with linear dimension 37.77 km and central and surface redshifts are 4.858 and 0.4524 respectively. We also study some well known regular solutions (T-4, D-1, D-2, H, A, P) of Einstein’s field equations in curvature coordinates with the feature of constant adiabatic sound speed. We have chosen those values of Schwarzschild parameter u for which, these solutions describe perfect fluid balls realistic equations of state. However, except (P) solution, all these solutions have monotonically non-decreasing feature of adiabatic sound speed. Hence (P) solution is having a well behaved model for uniform radial motion of sound. Keeping in view of well behaved nature of the solution for this feature and assuming the surface density; ρ _b =2×10¹⁴ g/cm³, the maximum mass of Neutron star comes out to be 1.34 M _Θ with linear dimension 28.74 km. Corresponding central and surface redshifts are 1.002 and 0.1752 respectively.     

A Fast Current-Field Iteration Method for Calculating Nonlinear Force-Free Fields

Existing methods for calculating nonlinear force-free magnetic fields are slow, and are likely to be inadequate for reconstructing coronal magnetic fields based on high-resolution vector magnetic field data from a new generation of spectro-polarimetric instruments. In this paper a new implementation of the current-field iteration method is presented, which is simple, fast, and accurate. The time taken by the method scales as N ⁴, for a three-dimensional grid with N ³ points. The method solves the field-updating part of the iteration by exploiting a three-dimensional Fast Fourier Transform solution of Ampere’s law with a current density field constructed to satisfy the required boundary conditions, and uses field line tracing to solve the current-updating part of the iteration. The method is demonstrated in application to a known nonlinear force-free field and to a bipolar test case.     

A new well behaved exact solution in general relativity for perfect fluid

We present a new spherically symmetric solution of the general relativistic field equations in isotropic coordinates. The solution is having positive finite central pressure and positive finite central density. The ratio of pressure and density is less than one and casualty condition is obeyed at the centre. Further, the outmarch of pressure, density and pressure-density ratio, and the ratio of sound speed to light is monotonically decreasing. The solution is well behaved for all the values of u lying in the range 0<u≤.186. The central red shift and surface red shift are positive and monotonically decreasing. Further, we have constructed a neutron star model with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. The maximum mass of the Neutron star comes out to be M=1.591 M _Θ with radius R _b ≈12.685 km. The most striking feature of the solution is that the solution not only well behaved but also having one of the simplest expressions so far known well behaved solutions. Moreover, the good matching of our results for Vela pulsars show the robustness of our model.     

Tilted Bianchi Type I stiff fluid magnetized cosmological model in general relativity

Tilted Bianchi Type I cosmological model for perfect fluid distribution in presence of magnetic field, is investigated. To get a determinate solution, it has been assumed that the universe is filled with stiff perfect fluid distribution together with A=(BC) ⁿ where A,B,C are metric potentials and n is a constant. The behaviour of the model in presence and absence of magnetic field is discussed. The various physical and geometrical aspects of the model, is also discussed. It has been shown that tilted nature of the Bianchi Type I model is preserved due to magnetic field. This revised version was published online in July 2006 with corrections to the Cover Date.     

Cylindrically symmetric inhomogeneous universe with electromagnetic field in string cosmology

Cylindrically symmetric inhomogeneous string cosmological model in presence of electromagnetic field is investigated. We have assumed that F ₂₃ is the only non-vanishing component of F _ij . To get the deterministic solution, it has been assumed that the expansion (θ) in the model is proportional to the eigen value σ ¹ ₁ of the shear tensor σ ⁱ _j . The physical and geometric aspects of the model are also discussed.      

Relativistic magnetofluid disc with nonzero radial velocity in Schwarzschild geometry

In this paper we consider the equilibrium of a magnetofluid disc in Schwarzschild background with an external magnetic field, having the azimuthal and the radial components of the flow velocity nonzero. The electrical conductivityσ of the fluid is taken to be finite and thus the solution for the electromagnetic field is required to satisfy the Ohm’s law too with the four-current having onlyJ ^ϕ andJ ^t nonzero. The various physical parameters that have to correlate for possible equilibrium configurations are identified and their respective magnitudes estimated. It is found that for a given angular momentum distribution the inner edge of the disc can reach well within the usual6m limit only when the surface magnetic field of the central object is not too high when the matter density at the outer edge of the disc and the accretion rate are taken with reasonable limits     

Exact solution to radiation-filled Brans-Dicke closed space cosmology

Under the assumption of a power law (k·R ⁿ=C,C=const.) between the gravitational constantk and the radius of curvatureR of the Universe and forP=1/3 the exact solution is sought for the cosmological equations of Brans and Dicke. The solution turns out to be valid for closed space and the parameter of the scalar-tensor theory is necessarily negative. The radius of curvature increases linearly with respect to the age of the Universe while the gravitational constant grows with the square of the radius of curvature. It has been shown (Lessner, 1974) that in this case (KR ²) the spatial component of the field equations is independent of the remaining equations. However, our solution satisfies this independent equation. This solution for the radiation-dominated era corresponds to the solution for the matter-dominated era found by Dehnen and one of the authors (Dehnen and Obregón, 1971). Our solution, as is the solution previously obtained for the matter-dominated era, is in contradiction to Dirac's hypothesis in which the gravitational constant should decrease with time in an expanding Universe.     

A new class of bulk viscous universe with time dependent deceleration parameter and Λ-term

A new class of exact solutions of Einstein’s field equations with a bulk viscous fluid for an LRS Bianchi type-Ia obtained by using a time dependent deceleration parameter and cosmological term Λ. The coefficient of bulk viscosity is assumed to be a power function of mass density (ξ=ξ ₀ ρ ⁿ ). We have obtained a general solution of the field equations from which six models of the universe are derived: exponential, polynomial and sinusoidal form respectively. The behaviour of these models of the universe are also discussed in the frame of reference of recent supernovae Ia observations.      

Exact solution of perfect fluid massive string cosmology in Bianchi type?III space-time with decaying vacuum energy density?Λ

Exact solution of Einstein’s field equations is obtained for massive string cosmological model of Bianchi III space-time using the technique given by Letelier (Phys. Rev. D 20:2414, 1983) in presence of perfect fluid and decaying vacuum energy density Λ. To get the deterministic solution of the field equations the expansion θ in the model is considered as proportional to the eigen value s² ₂\sigma^{2}_{~2} of the shear tensor s^j _i\sigma^{j}_{~i} and also the fluid obeys the barotropic equation of state. The vacuum energy density Λ is found to be positive and a decreasing function of time which is supported by the results from recent supernovae Ia observations. It is also observed that in early stage of the evolution of the universe string dominates over the particle whereas the universe is dominated by massive string at the late time. Some physical and geometric properties of the model are also discussed.     

Similarity solution for unsteady accretion flow

Similarity solution for unsteady accretion flow in a gravitational field of a point mass is obtained. Characteristic features of the flow pattern are discussed. It is shown that the shock waves appeared in the accretion flow propagate outward asr _s t ^2/3.     

Towards a cosmic no hair theorem for higher-order gravity

We use gravitational Lagrangians R□^k √− g and linear combinations of them motivated from trials how to overcome the non- renormalizability of Einstein' s theory. We ask under which circumstances the de Sitter space- time represents an attractor solution in the set of spatially flat Friedman models. This property ensures the inflationary model to be a typical solution; nowadays, this property is called cosmic no hair theorem because it is analogous to the no hair theorem for black holes. Results are: for arbitrary k, i.e., for arbitrarily large order 2k + 4 of the field equation, one can always find examples where the attractor property takes place. Such examples necessarily need a non- vanishing R²- term. The main formulas do not depend on the dimension, so one gets similar results also for 1+1- dimensional gravity and for Kaluza- Klein cosmology.     

Massless scalar field in Robertson-Walker space-time

Recently, exact spatially-homogeneous solutions have been found for a conformally invariant massless scalar fieldS(t) coupled to a Robertson-Walker geometry. We investigate extending these solutions to inhomogeneous scalar fieldsS(t, x ^l ). For an isotropic scalar fieldS(t, r) we find a solution satisfying three of the five field equations. If we use REDUCE, we show that the remaining equations forceS=S(t).     

Fast oscillations and particle acceleration in the neutral sheet

This paper suggests that fast periodic oscillations in the neutral sheet occur after it is perturbed strongly. An analytic solution of the oscillation process, of which the period T is about 1 ms, is obtained on the basis of the snow-plow model. This dynamical process causes the periodic appearance and disappearance of a diffusive region in the sheet. A time interval t, during which the diffusive region exists, is about 10^–2-10^–3 T. Under the assumption of a relatively weak electric field and the spectrum index = 1 of Langmuir turbulence, we obtain an analytic solution of the quasi-linear equation of the distribution function of particles with a periodic electric field. We show that the combined acceleration by the electric field and turbulence can produce the periodic streams of energetic electrons. Their energy can reach about 50 keV. These periodic streams of electrons could produce the microwave millisecond spike emission.     

Polarization of continuum radiation in magnetic atmospheres

A numerical solution is presented for the problem of continuum radiative transfer in a magnetoactive medium. The continuum opacities are calculated in the presence of a strong magnetic field (H=10⁷ G) typical of magnetic white dwarfs. The L.T.E. pure absorption model is assumed for calculating the polarized radiation field emitted by a realistic model atmosphere in the plane parallel approximation. The wavelength dependence of the linear and circular polarizations are calculated for both uniform and dipole field configurations.     

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.     

Verification of maximum limit of density variation parameter λ for a stable neutron star using Reissner-Nordström interior solution

A static spherically-symmetric model, based on an exact solution of Einstein's equation, gives the permissible matter density ~2 × 10¹⁴ g cm^–3. By use of the change in radius density (i.e., central density per unit radius) minimum, Parui and Sarma (1991) have estimated the upper limit of the density variation parameter = 0.68 for a superdense star such as a neutron star withK = –2. In this paper we have verified this upper limit using the Reissner-Nordström interior solution of the Einstein-Maxwell's field equations withK = - 3.