Revisiting the classical electron model in general relativity

Motivated by earlier studies (Tiwari et al. in Astrophys. Space Sci. 182:105, 1984; Herrera and Varela in Phys. Lett. 189:11, 1994), we model electron as a spherically symmetric charged perfect fluid distribution of matter. The existing model is extended assuming a matter source that is characterized by quadratic equation of state in the context of general theory of relativity. For the suitable choices of the parameters, our charged fluid models almost satisfy the physical properties of electron.     

Magnetohydrodynamical model of pulsar rotation. Exact periodic solutions

A rotaing rigid body with elipsoidal cavity filled with magnetic fluid is considered as a pulsar model. Dynamical equations for the pulsar model are derived and investigated, certain integrable cases are indicated. Three–parameter sets of periodic solution integrable in terms of elliptic functions of the time variable are obtained. A formula is derived for the period of rotation and magneto–rotational oscillations of the pulsar.     

Exact solutions of a flat cosmological model in BSTT

We solve the cosmological equations for the bimetric scalar—tensor theory of gravitation (BSTT) for a flat model of the Friedmann type with the equation of state p = a. In the initial stage of expansion, the energy density of the scalar field dominates over the energy density of matter. As a result, the behavior of the solution in this limit does not depend on a. For later stages of expansion of the Universe, the solution obtained goes to a special solution having the form of a power law function of time. In this case, the relative change in the gravitational scalar is proportional to the Hubble parameter. In the limit of large values for the parameter of the theory, only a simple solution with zero value of the constant of integration goes to the corresponding Friedmann solution of general relativity theory.Translated from Astrofizika, Vol. 37, No. 2, pp. 351–362, April–June, 1994.I would like to thank L. Sh. Grigoryan for valuable discussions and support.     

Comments on revisiting the classical electron model in general relativity

We point out here that all the solutions presented in Rahaman et al. (Astrophys. Space Sci. 331:191–197, 2011) are incorrect and do not satisfy the system of governing Einstein-Maxwell field equations.     

Slowly-rotating charged viscous-fluid universes: Exact solutions

By considering a spherically-symmetric metric, certain new analytic solutions for charged rotating viscous-fluid cosmological models in the Einstein universe are found out. Five different cases in which the nature and role of the rotational velocity (r, t) is related to the local dragging of inertial frames and that of matter rotation (r, t), are investigated. Except for the case of perfect dragging, the electric field is found to have a damping effect on the rotation of matter. The damping effect is seen to be roughly analogous to the viscosity. In some solutions we find out the temporal restrictions for realistic astrophysical situations. Models which are rotating as well as expanding are also obtained and studied.     

Exact Brans-Dicke-Bianchi type-VIIh solutions

We discuss the Brans-Dicke-Bianchi type-VII_h field equations. Exact solutions are given for the vacuum case as well as for the stiff matter case. The derived solutions are the generalizations of the GRT-solutions first given by Doroshkevichet al. (1973) and Lukash (1974a). In addition we present a new BDT-stiff matter solution which has no analogy in the GRT.     

Exact self-creation cosmological solutions

Under the assumption of a power law between the expansion factor of the Universe and the scalar field of the second self-creation theory proposed by G. A. Barber, the cosmological equations are reduces to quadratures. Several exact solutions are obtained, among them linearly expanding and inflationary universes with a barotropic equation of state.     

Exact five-dimensional cosmological solutions

We derive some new perfect solutions in five dimensions. The solutions given are the generalizations of theL(4, 7) vacuum solution given recently by Demaret and Hanquin (1985) in an incorrect form only.     

Analytic neutron stars in general relativity: Exact solutions for the non-homogeneous charged model

We have extended the so-called Adams' method to the non-homogeneous charged model of neutron stars. Numerical applications have been compared with results obtained for a given equation of state.     

Exact anisotropic polytropic cylindrical solutions

In this paper, we study anisotropic compact stars with static cylindrically symmetric anisotropic matter distribution satisfying polytropic equation of state. We formulate the field equations as well as the corresponding mass function for the particular form of gravitational potential \(z(x)=(1+bx)^{\eta }~(\eta =1,~2,~3)\) and explore exact solutions of the field equations for different values of the polytropic index. The values of arbitrary constants are determined by taking mass and radius of compact star (Her X-1). We find that resulting solutions show viable behavior of physical parameters (density, radial as well as tangential pressure, anisotropy) and satisfy the stability condition. It is concluded that physically acceptable solutions exist only for \(\eta =1,~2\).     

Exact solutions to Kaluza-Klein cosmologies

We consider general methods to find exact solutions of Kaluza-Klein cosmologies with phenomenological matter and show some general conclusions about factorwise homogeneous and isotropic models.     

Exact solutions for magnetized black holes

The Ernst-Wild solution with conical singularities removed is discussed. The physical quantities characterizing the modified solution including electromagnetic four-potential, electric, and magnetic field fluxes through the upper hemisphere of the horizon, equatorial and meridional circumferences on the horizon are calculated.     

Exact solutions in brans-dicke theory: A dynamical system approach

A method is furnished for constructing isotropic and homogeneous solutions in Brans-Dicke theory based on the analysis of the dynamical system formed by the field equations. Large classes of solutions found in the literature are recovered and shown to be special cases of those generated by this method.Research partially supported by CNPq, Brazil.     

Exact solutions for friedmann models with radiation

Exact expressions are given for the properties of the general expanding Friedmann model universe with non-zero cosmological constant and containing non-interacting matter and radiation.     

Exact solutions in Jordan-Brans-Dicke homogeneous universes I

Spatially homogeneous, anisotropic Bianchi types I-II-III-V-VI_o-VI_h and Kantowski-Sachs (KS) are shown to have perfect fluid solutions in Jordan-Brans-Dicke (JDB) cosmological theory. All the solutions obey the relation =a²+b+c, where and are the re-scaled energy density and the re-scaled scalar field, respectively, and is a time parameter. This relation is derived in Bianchi type-I and gives rise to the general solution for this model universe. In the remaining Bianchi types this same relation is shown to hold as well; and new solution, some of which do not possess locally rotational symmetry, are obtained.     

Exact perfect fluid solutions in the Brans-Dicke-theory

We present the general stiff matter and radiation solutions for thek=0, 1, –1 Friedmann-Robertson-Walker space-times in the Brans-Dicke scalar-tensor theory.     

Exact solutions: neutral and charged static perfect fluids with pressure

We show in this article that charged fluid with pressure derived by Bijalwan (Astrophys. Space. Sci. doi:, 2011a) can be used to model classical electron, quark, neutron stars and pulsar with charge matter, quasi black hole, white dwarf, super-dense star etc. Recent analysis by Bijalwan (Astrophys. Space. Sci., 2011d) that all charged fluid solutions in terms of pressure mimic the classical electron model are partially correct because solutions by Bijalwan (Astrophys. Space. Sci. doi:, 2011a) may possess a neutral counterpart. In this paper we characterized solutions in terms of pressure for charged fluids that have and do not have a well behaved neutral counter part considering same spatial component of metric e ^λ for neutral and charged fluids. We discussed solution by Gupta and Maurya (Astrophys. Space Sci. 331(1):135–144, 2010a) and solutions by Bijalwan (Astrophys. Space Sci. doi:, 2011b; Astrophys. Space Sci. doi:, 2011c; Astrophys. Space Sci., 2011d) such that charged fluids possess and do not possess a neutral counterpart as special cases, respectively. For brevity, we only present some analytical results in this paper.     

Exact MHD solutions for rotating,magnetic stars

Simple exact solutions of the magnetohydrodynamic equations are found for rotating, magnetic stars. The velocity and magnetic field are axisymmetric and purely toroidal, and the magnetic energy density equals the kinetic energy density. For constant mass density, the solution reduces to that of Chandrasekhar (1956), which is stable even against non-axisymmetric perturbations. For an ideal gas equation of state, the condition for radiative thermal equilibrium is solved to lowest order in the non-spherical perturbation. The velocity, magnetic field and non-spherical pressure and temperature perturbations all vanish within cones centered around the rotation axis, |cos |>x _i a zero of a Legendre polynomial. Low-order, long-period stellar oscillations may be excited by MHD instabilities near the equatorial region which become damped near the axis.     

Exact self-similar Bianchi II solutions for some scalar-tensor theories

We study how may behave the gravitational and the cosmological “constants”, (G and Λ) in several scalar-tensor theories with Bianchi II symmetries. By working under the hypothesis of self-similarity we find exact solutions for three different theoretical models, which are: the Jordan-Brans-Dicke (JBD) with Λ(?), the usual JBD model with potential U(?) (that mimics the behavior of Λ(?)) and the induced gravity (IG) model proposed by Sakharov and Zee. After a careful study of the obtained solutions we may conclude that the solutions are quite similar although the IG model shows some peculiarities.     

Exact non-flat Friedmann-Robertson-Walker solutions in Barker's theory of gravitation

We derive the complete series of thek=0, 1, –1 Friedmann-Robertson-Walker vacuum solutions in Barker's theory of gravitation. Only thek=0 solution was known in a somewhat different form.