Charged fluid sphere in bimetric general theory of relativity

Static and spherical symmetric solutions of the field equations in the bimetric general theory of gravitation are obtained for perfect and anisotropic charged fluids under the assumption that the physical metric admits a one-parameter group of conformal motion. All solutions are matched to the Reissner–Nordstrom metric and possess positive energy density larger than the stresses, everywhere within the sphere. The solution agrees with Einstein’s general relativity for a physical system comparable to the size of the universe, such as the solar system.     

Extremization of mass of charged superdense star models describe by Durgapal type space-time metric

In the present article, we have obtained a class of charged superdense star models, starting with a static spherically symmetric metric in curvature coordinates by considering Durgapal (J. Phys. A 15:2637, 1982) type metric i.e. g ₄₄=B(1+Cr ²) ⁿ , where n being any positive integer. It is observed that the maximum mass of the charged fluid models is monotonically increasing with the increasing values of n≤4. For n≥4, the maximum mass of the charged fluid models is throughout monotonically decreasing and over all maximum mass is attained at n=4. The present metric tends to another metric which describes the charged analogue of Kuchowicz neutral solution as n→∞. Consequently the lower limit of maximum mass of the charged fluid models could be determined and found to be 5.1165 solar mass with corresponding radius 18.0743 Km. While the upper limit of maximum mass of the model of this category is already known to be 5.7001 solar mass with corresponding radius 17.1003 Km for n=4. The solutions so obtained are well behaved.     

A family of charge analogue of Durgapal solution

We obtain a new parametric class of exact solutions of Einstein–Maxwell field equations which are well behaved. We present a charged super-dense star model after prescribing particular forms of the metric potential and electric intensity. The metric describing the super dense stars joins smoothly with the Reissner–Nordstrom metric at the pressure free boundary. The electric density assumed is where n may take the values 0,1,2,3,4 and so on and K is a positive constant. For n=0,1 we rediscover the solutions by Gupta and Maurya (Astrophys. Space Sci. 334(1):155, 2011) and Fuloria et al. (J. Math. 2:1156, 2011) respectively. The solution for n=2 have been discussed extensively keeping in view of well behaved nature of the charged solution of Einstein–Maxwell field equations. The solution for n=3 and n=4 can be also studied likewise. In absence of the charge we are left behind with the regular and well behaved fifth model of Durgapal (J. Phys. A 15:2637, 1982). The outmarch of pressure, density, pressure-density ratio and the velocity of sound is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. For this class of solutions the mass of a star is maximized with all degree of suitability, compatible with Neutron stars and Pulsars.     

Relativistic modeling of the neutron star in Vela X-1 via Bardeen space-time satisfying the embedding condition

In this paper, we present two new exact and analytic solutions of the Einstein–Maxwell field equations describing compact anisotropic charged stars satisfying the Karmarkar condition in the background of Bardeen black hole geometry. The solutions are composed of two parts: The inner region of the star is described by class I Karmarkar space-time, while exterior of the star is characterized by both the Bardeen and the Reissner–Nordstrom space-times. Physical analysis of the matter and thermodynamical variables show that the models are well-behaved. For our parametric set of values, we conclude that the Bardeen black hole metric can be used as an alternate to the exterior Reissner–Nordstrom metric.     

Duality rotations and type D solutions of Einstein-Born-Infeld theory

Within the non-linear electrodynamics of Born-Infeld type, constrained by the condition that admits the freedom of the duality rotations the explicit type D solutions, which generalize the charged Taub-NUT metric with cosmological constant, are constructed. The obtained type D solution exhausts all solutions within the considered class, assumed that the real eigenvectors of the electromagnetic field are aligned along the geodesic and shear-free principa null directions.     

Some rotating perfect fluid universes coupled with electromagnetic field interacting with gravitation

Some new interesting solutions, the dynamics, behaviour and phenomena of rotating charged perfect fluid models are investigated, and their physical and geometrical properties are studied in order to substantiate the possibility of the existence of such astrophysical bodies in this Universe. The nature and role of the metric rotation Ω(r,t) as well as that of the matter rotation ω(r,t) are studied for uniform and non-uniform motions. The reactions of the gravitational and charged fields with respect to the rotational motion are studied and possible results are explored for real astrophysical situations, and in some solutions we find the spatial restrictions on the models for realistic conditions. Rotating models which are expanding are obtained in which the rotational motions are decaying with time.     

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 cylindrically symmetric solutions in Rastall theory of gravity

In this paper, we explore some exact cylindrically symmetric solutions in the context of Rastall theory of gravity. For this purpose, we consider the general form of a metric in the cylindrical Weyl coordinates. The modified field equations are developed in the presence of charge. In particular, we try to recover the well-known Levi–Civita’s static cylindrically symmetric solution in the framework of Rastall gravity. The graphical behavior of energy density and pressure component is presented along with the discussion of energy conditions. Finally, the solutions in the context of general relativity are discussed. It is concluded that Levi–Civita’s static cylindrically symmetric charged solutions do exist in Rastall theory of gravity.     

A further generalization of Vaidya''s star metric

In this paper, a metric containing five arbitrary functions of time is obtained which describes the gravitational field of an arbitrary accelerated and charged point-mass (star). It is a further generalization of Vaidya's star metric, [1]. In particular cases, it reduces to the Reissner-Nortström metric and the Kinnersley metric [2]. Since the various parameters of the source can vary arbitrarily in time, this metric is of wide applicability and may prove to be useful for various specific astronomical objects.     

Rotating charged perfect-fluid universes coupled with scalar field in general relativity

Certain new analytic solutions for slowly-rotating charged perfect-fluid universes coupled with zero-mass scalar field are found out to substantiate the possibility of the existence of rotating cosmological objects of such nature and their dynamics is investigated. The nature and role of the metric rotation (r, t) as well as that of the matter rotation (r, t) under different conditions are studied. The effects of the charged field and the scalar field on the rotational motion are also discussed. In some solutions we find out the temporal restrictions on the models for real astrophysical situations. Rotating models which are expanding as well are obtained, in which cases the rotational velocities are found to decay with the time, and these models may be taken as good examples of real astrophysical objects in this Universe.     

Closed form charged fluid with t = constant hypersurfaces as spheroids and hyperboloids

In the present article models of well behaved charged superdense stars with surface density 2×10¹⁴ gm/cm³ are constructed by considering a static spherically symmetric metric with t = const hypersurfaces as spheroids and hyperboloids. Maximum mass of the star is found to be 7.66300M _Θ with radius 19.35409 km for spheroids case while 1.51360M _Θ with radius 13.72109 km for hyperboloid case satisfying ultra-relativistic conditions. The solutions thus found satisfy all the reality and causality conditions. For brevity we don’t present a detailed analysis of the derived solutions in this paper.     

Charged isotropic model with conformal symmetry

We investigate the behaviour of a charged isotropic model with conformal symmetry. The relationship between the gravitational potentials arising from the conformal condition is used to generate a new class of exact solutions to the Einstein-Maxwell equations. A specific form of the electric field intensity and the metric potential is required to avoid a singularity at the centre. We can find simple elementary functions for the matter variables and the potentials with realistic profiles. The causality conditions, stability conditions and energy conditions are satisfied. Masses, radii, central densities and surface redshifts are generated, and the values are consistent with the compact stars 4U 1538-52 and PSR J1614-2230.     

Gravitational sources of purely electromagnetic origin

The Einstein-Maxwell field equations for charged dust corresponding to static axially-symmetric metric of Levi-Civita have been studied. It has been shown that when the metric potentialsg _ij are functions of only one of the coordinates, viz.,r, the interior charged dust becomes purely of electromagnetic origin, in the sense that the physical quantities like the energy density, the effective gravitational mass, etc., are dependent only on the charge density and vanish when this charge density vanishes. Such models are known as electromagnetic mass models in the classical electrodynamics. An interior charged dust solution corresponding to this case has been obtained which, in a sense, represents an infinite dust distribution of electromagnetic origin. In the second case, viz., when the metric potentials are functions of the coordinatesr andz both, it has been shown that some of the situations correspond to electromagnetic mass models. An example to illustrate this case has been obtained. This represents the source of the Reissner-Nordström-Curzon field (an analogue of the Reissner-Nordström solution obtained by Curzon) which according to Curzon describes the exterior field of an electron.     

Surface temperature of a rotating charged body

The surface temperature of a rotating, charged body is found separately under the Kerr-Newman metric and the vector graviton metric. Particular reference is made to pulsars. It is found that, 1) under the Kerr-Newman metric, the surface temperature rises from the poles to the equator, when the radius R of the body is greater than a certain critical value, r_n. When R= r_n, the surface temperature is uniform. When R < r_n, the above gradient is reversed. For pulsars, the equatorial temperature is some 3 × 10⁴ K higher than the polar temperature. 2) Under the Vector graviton field metric, a similar temperature differential exists, but it is much smaller in size.     

Field of a charged particle in a scalar-tensor theory of gravitation

Field equations in the scalar-tensor theory of gravitation, proposed by Saez and Ballester (Phys. Lett. A 113: 467, 1986), are obtained for a static charged point mass with the aid of a spherically symmetric metric. A closed form exact solution of the field equations is presented and may be considered as describing the field due to a charged mass point at the origin surrounded by a scalar-tensor field.     

A family of exact solutions of Einstein-Maxwell field equations in isotropic coordinates: an application to optimization of quark star mass

In the present paper, we have obtained a class of charged super dense star models, starting with a static spherically symmetric metric in isotropic coordinates for perfect fluid by considering Hajj-Boutros (in J. Math. Phys. 27:1363, 1986) type metric potential and a specific choice of electrical intensity which involves a parameter K. The resulting solutions represent charged fluid spheres joining smoothly with the Reissner-Nordstrom metric at the pressure free interface. The solutions so obtained are utilized to construct the models for super-dense star like neutron stars (ρ _b =2 and 2.7×10¹⁴ g/cm³) and Quark stars (ρ _b =4.6888×10¹⁴ g/cm³). Our solution is well behaved for all values of n satisfying the inequalities \(4 < n \le4(4 + \sqrt{2} )\) and K satisfying the inequalities 0≤K≤0.24988, depending upon the value of n. Corresponding to n=4.001 and K=0.24988, we observe that the maximum mass of quark star M=2.335M _⊙ and radius R=10.04 km. Further, this maximum mass limit of quark star is in the order of maximum mass of stable Strange Quark Star established by Dong et al. (in arXiv:1207.0429v3, 2013). The robustness of our results is that the models are alike with the recent discoveries.     

Effects of electromagnetic field on shearfree spherical collapse

This paper is devoted to study spherically symmetric shearfree charged gravitational collapse with radial heat flux and isotropic pressure. For the matching of the interior spacetime, we take Vaidya-Reissner-Nordström metric outside the spherical system. We solve the field equations numerically by taking ansatz on the metric functions and using Darmois junction conditions. The behavior of density, pressure, radial heat flux, luminosity and the mass function is analyzed. Finally, we check validity of the energy conditions through plots.     

Perfect-fluid sources for the Levi-Civita metric

Cylindrically symmetric perfect fluid solutions are derived for the Levi-Civita metric. The pressure P is finite. The matter density is greater than the stresses in the material. The solutions are inside cylinders of bounded radius at which the pressure vanishes. The range of σ, for which the sources have been matched to the Levi-Civeta metric is ∞>σ>0. The solutions are regular and satisfy energy conditions     

Cosmological viscous fluid universe in slow rotation

The problem of slowly rotating cosmological viscous fluid universe in a homogeneous and isotropic models has been investigated by considering the perturbation in the metric rotation function to the first order of smallness associated with certain physical restrictions imposed on the metric rotation function and matter angular velocity. Some more general solutions for the metric rotation function have been obtained and physical interpretation of the solutions have been investigated.