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.     

A study of massive classical polytropes in general relativity

A detailed study of classical polytropes in general relativity has been presented for _O ((dP/dE)_O) 1.0 and _O((P/E _O)_O. The behaviour of various structural parameters with _O/_O, _O and _O are the values ofP/E and dP/dE at the centre) has been studied. The most important result of this study is the fact the qualitative behaviour of all the structural parameters depends only on the value of µ_O for the various assigned _O values. The maximum value of surface red shift occurs when µ_O=0.6 and for _O=1.0 it equals 0.618. These structures are gravitationally bound for µ_O0.8 and most so for µ_O=0.4. The maximum value of binding coefficient comes out to be 0.181 when _O=1.0. These structures have been used to model neutron stars. The maximum mass of neutron star based upon such a model comes out to be 2.55M (for µ_O=0.4 and _O=1.0) and maximum size comes out to be 15.0 km (for µ_O=0.2 and _O=1.0). It is also seen that the structures are pulsationally stable for µ0.6.     

Cosmological mass model in general relativity

Relativistic cosmological field equations are obtained for a non-static stationary Bertotti-Robinson-type space-time for interacting perfect fluid and electromagnetic field. The cosmological solution to the field equations are obtained and the nature of the electromagnetic field as well the perfect fluid are studied. The electromagnetic field generated here corresponds to a special generic case and the perfect fluid distribution degenerates into a barotropic perfect fluid with equation of statep+=0, >0. It is shown here that the interacting barotropic fluid can generate gravitation only when the cosmological constant being a function ofx in a dynamic field.     

FLRW non-singular cosmological model in general relativity

A singularity free cosmological model is obtained in a homogeneous and isotropic background with a specific form of the Hubble parameter in the presence of an interacting dark energy represented by a time-varying cosmological constant in general relativity.Different cases that arose have been extensively studied for different values of the curvature parameter.Some interesting results have been found with this form of the Hubble parameter to meet the possible negative value of the deceleration parameter(-1/3 q 0) as the current observations reveal.For some particular values of these parameters,the model reduces to Berman's model.     

The inflationary Kantowski-Sachs cosmological model in general relativity

In this paper, we have investigated the inflationary Kantowski-Sachs cosmological model in the presence of mass less scalar field with a flat potential. To get an inflationary solution, we have considered a flat region of a constant potential V. Some physical and kinematical properties of the model are studied.     

Bianchi Type-III stiff fluid cosmological model in general relativity

In this paper, we have investigated a tilted Bianchi Type-III stiff fluid cosmological model in general relativity. To get a determinate solution, we have assumed a condition A=(BC) ⁿ between metric potentials. The various physical and geometrical aspects of the model are discussed.     

On slowly-rotating cosmological viscous-fluid model universes in general relativity

The dynamics of a slowly-rotating cosmological viscous-fluid universe is investigated and the rotational perturbations of such models are studied in order to substantiate the possibility that the Universe is endowed with slow rotation, in the course of presentation of some new analytic solutions. Three different cases are taken up in which the nature and role of the metric rotation (r, t) as well as that of the matter rotation (r, t) are discussed. The periods of physical validity of some of the models and the effect of viscosity on the rotational motion are also found out. Rotating models which are expanding as well are obtained, where in all the cases the rotational velocities are found to decay with the time; and these models may be taken as good examples of real astrophysical situations.     

Magnetostatic stiff-fluid model of cylindrical symmetry in general relativity

We study the static stiff-fluid model for perfect fluid distributions in the presence of incident magnetic field. The magnetic field is surrounded by static stiff fluid of infinite electric conductivity and it is due to the electric current flowing along theZ-axis. The various physical and geometrical properties together with the state of model in absence of magnetic field are also discussed.     

A magnetized homogeneous inflationary cosmological model in general relativity

In this paper we have investigated the effect of magnetic field on an orthogonal Bianchi type-I inflationary cosmological model using the concept of Higgs field. It has been investigated that the expansion and inflation in the model increases as the magnetic field increases. To get inflationary model we have assumed a mass less scalar field with flat potential V(φ)that has flat region. This revised version was published online in July 2006 with corrections to the Cover Date.     

Exact solutions: classical electron model

Rahaman et al. (Astrophys. Space. Sci. 331:191–197, 2010) discussed some classical electron models (CEM) in general relativity. Bijalwan (Astrophys. Space. Sci. 334:139–143, 2011) present a general exact solution of the Einstein-Maxwell equations in terms of pressure. We showed that charged fluid solutions in terms of pressure are not reducible to a well behaved neutral counter part for a spatial component of metrice ^λ . Hence, these solutions represent an electron model in general relativity. We illustrated solutions in terms of pressure briefly with de-Sitter equation of state and charged analogues of Kohler Chao interior solution as a special cases.     

Magneto-viscous fluid cosmological model of plane symmetry in general relativity

The object of this paper is to investigate the behaviour of magnetic field in a viscous fluid cosmological model. Various physical and geometrical properties of the model have also been discussed.     

Expanding and shearing magneto-viscous fluid cosmological model in general relativity

The object of this paper is to investigate the behavior of a magnetic field in a viscous fluid cosmological model. It has been assumed that the expansion () is proportional to the eigenvalue ₁ of the shear tensor _i ^j and the coefficient of shearing viscosity is proportional to the scalar of expansion. The paper also discusses the behavior of the model when the magnetic field tends to zero and comments on some other physical properties.     

Radiating anisotropic two-fluid model universes involving rotation in general relativity

Radiating anisotropic two-fluid model universes coupled with a scalar field when a slow rotation is introduced in them are studied here, where the anisotropic pressure is generated by the presence of two non-interacting perfect fluids which are in relative motion with respect to each other. Special discussion is made of the physically interesting class of models in which one fluid is a comoving radiative perfect fluid which is taken to model the cosmic microwave background and the second a non-comoving perfect fluid which will model the observed material content of the Universe. Here we take up four analytic solutions. The effects of rotation on these models are studied and the reactions of the scalar and the radiation fields with respect to the rotational motion are discussed. Analysis on the rotational perturbations are also made, in the course of which the amount of anisotropy induced in the pressure distribution by a small deviation from the Friedmann metric is also investigated. It is shown that such anisotropies could grow faster than the expansion of the Universe. The rotating models we obtain here are found to be theoretically satisfactory and they may be taken as physically acceptable models.     

A model of an exploding,radiating star in general relativity

In a previous paper Adams, Cary and Cohen (1994) presented a model of a supernova. In that paper the equations of General Relativity describing the evolution of a spherically symmetric, radiating star were solved analytically. The evolution of the star was determined by the application of boundary conditions at the center and at the edge. Due to lmitations in the presupernova model, only the very slow inward motion of an unstable, degenerate core could be considered. The solution was also limited by the need to exclude a runaway term, one that increased exponentially with time. Without the exclusion of the runaway, the luminosity would have increased without bound and the mass would have become negative.This paper presents a completely analytic solution to the equations of General Relativity describing the evolution of a Type II supernova. Professor S.E. Woosley kindly gave us data on the physical variables of a 12M ₀ presupernova star. In our model the core collapses within 1 s, leaving a 1.3M ₀ remnant. Shortly afterward 10.6M ₀ is ejected to infinity, and 0.17M ₀ is radiated away in the form of neutrinos. The distance of the edge from the center increases proportionally to the two-thirds power of the time. The luminosity decreases proportionally to the inverse four-thirds power.Although the runaway solution was modified by the exploding rather than a static envelope, it must still be excluded by adjusting initial conditions. Its character is changed from an exponential to a very large power (55) of time. The removal of a degree of freedom by this exclusion leads to physically non-sensical results such as negative luminosity. The inclusion of a term describing motion of the mantle due to neutrino interactions provides the additional degree of freedom necessary for physically reasonable results.     

Inhomogeneous viscous fluid cosmological model with electromagnetic field in general relativity

The object of this paper is to investigate the behaviour of electromagnetic field in inhomogeneous cosmological models obtained for viscous fluid distributions. The various particular cases when both the electromagnetic and viscosity are absent, are also discussed.     

Isentropic stars in general relativity

In an investigation of the evolution of homogeneous, isentropic, stars through stages of diminishing entropy, Rakavy and Shaviv (1968) have recently found that stars of mass less thanM _c (Chandrasekhar's limiting mass for white dwarfs) evolve into white dwarfs, while stars of mass greater thanM _c approach a (singular) state of minimum entropy. An elementary explanation of these results is given and qualitative effects of general relativity are discussed. It is found that stars which are lighter than the Oppenheimer and Volkoff (1939) limit become white dwarfs, while heavier stars must become dynamically unstable at a finite stage in their evolution.     

Equilibrium ensembles in general relativity

Consider a collection of particles that interact only via elastic point collisions in a fixed background spacetime in the presence of some specified external fields. If there exists a time-like vector field that Lie derives the metric and the external fields, then it is possible to formulate sensible covariant analogues of the standard equilibrium ensembles from Newtonian statistical mechanics.     

Magneto-dipole configurations in general relativity

The solution of the system of Maxwell-Einstein equations, which determines the external gravitational and electromagnetic fields of magneto-dipole configurations, has been obtained to a quadratic approximation of magnetic momentum.     

Plane-symmetric universes in general relativity

Plane-symmetric solutions of Einstein's field equations in vacuum, in the presence of electromagnetic fields and with cosmological constant are explored in null coordinates. The gravitational field of an infinite plane (uncharged and charged both) is thus obtained in a simple and systematic way. The method adopted for these solutions has possibilities of generalization.