Solutions Of Einstein-Maxwell Field Equations Research Articles

Maximum mass of anisotropic charged strange quark stars in a higher dimensional approach (D ≥ 4)

In this article, a new class of solutions of Einstein-Maxwell field equations of relativistic strange quark stars obtained in dimensions , is shown. We assume that the geometry of space-time is pseudo-spheroid, embedded in Euclidean space of dimensions. The MIT bag model equation of state is employed to study the relevant properties of strange quark stars. For the causal and non-negative nature of the square of the radial sound velocity , we observe that some restrictions exist on the reduced radius , where R is a parameter related to the curvature of the space-time, and b is the radius of the star. The spheroidal parameter λ used here defines the metric potential of the component, which is pseudo-spheroidal in nature. We note that the pressure anisotropy and charge have some effects on λ. The maximum mass for a given surface density () or bag constant assumes a maximum value in dimension and decreases for other values of D. The generalized Buchdahl limit for a higher dimensional charged star is also obeyed in this model. We observe that in this model, we can predict the mass of a strange quark star using a suitable value of the electric charge (Q) and bag constant (B). Energy and stability conditions are also satisfied in this model. Stability is also studied considering the dependence of the Lagrangian perturbation of radial pressure () on the frequency of normal modes of oscillations. The tidal Love number and tidal de-formability are also evaluated.

New exact static solutions of Einstein-Maxwell field equations with a magnetic dipole

The Bonnor field shed light on imposition of two magnetic poles, both with mass m, and strengths -m and m, that are situated at a coordinate distance 2b on a symmetry axis. With the addition of an external magnetic field, these magnetic monopoles can be kept apart in an equilibrium. The new exact solutions of Einstein-Maxwell field equations in pure magnetic fields, in correspond to the Bonnor metric, are obtained in spherical coordinates with the use of Lie symmetry method. The obtained solutions are accelerating static solutions of Einstein-Maxwell equations in a more general form, for a semi-Riemannian manifold which is not conformally flat. The graphical representations in 3D are also shown.

Impact of generalized polytropic equation of state on charged anisotropic polytropes

In this paper, generalized polytropic equation of state is used to get new classes of polytropic models from the solution of Einstein-Maxwell field equations for charged anisotropic fluid configuration. The models are developed for different values of polytropic index n=1,~frac{1}{2},~2. Masses and radii of eight different stars have been regained with the help of developed models. The speed of sound technique and graphical analysis of model parameters is used for the viability of developed models. The analysis of models indicates they are well behaved and physically viable.

Models of Collapsing and Expanding Cylindrical Source in f(R,T) Theory

We discuss the collapsing and expanding solutions of anisotropic charged cylinder in the context of f(R,T) theory (R represents the Ricci scalar and T denotes the trace of energy-momentum tensor). For this purpose, we take an auxiliary solution of Einstein-Maxwell field equations and evaluate expansion scalar whose negative values lead to collapse and positive values give expansion. For both cases, the behavior of density, pressure, anisotropic parameter, and mass is explored and the effects of charge as well as model parameter on these quantities are examined. The energy conditions are found to be satisfied for both solutions.

Some Solutions of Einstein-Maxwell Field Equations for Charged Fluid Sphere

Some Solutions of Einstein-Maxwell Field Equations for Charged Fluid Sphere

Gravitational collapse and expansion of charged anisotropic cylindrical source

In this paper, we have discussed the gravitational collapse and expansion of charged anisotropic cylindrically symmetric gravitating source. To this end, the generating solutions of Einstein-Maxwell field equations for the given source and geometry have been evaluated. We found the auxiliary solution of the filed equations, this solution involves a single function which generates two kinds of anisotropic solutions. Every solution can be expressed in terms of arbitrary function of time that has been chosen arbitrarily to fit the various astrophysical time profiles. The existing solutions predict gravitational collapse and expansion depending on the choice of initial data. Instead of base to base collapse, in the present case, wall to wall collapse of the cylindrical source has been investigated. We have found that the electromagnetic field is responsible for the enhancement of anisotropy in collapsing system.

Effects of electromagnetic field on the collapse and expansion of anisotropic gravitating source

This paper is devoted to study the effects of electromagnetic on the collapse and expansion of anisotropic gravitating source. For this purpose, we have evaluated the generating solutions of Einstein-Maxwell field equations with spherically symmetric anisotropic gravitating source. We found that a single function generates the various anisotropic solutions. In this case every generating function involves an arbitrary function of time which can be chosen to fit several astrophysical time profiles. Two physical phenomenon occur, one is gravitational collapse and other is the cosmological expanding solution. In both cases electromagnetic field effects the anisotropy of the model. For collapse the anisotropy is increased while for expansion it deceases from maximum value to finite positive value. In case of collaps there exits two horizons like in case of Reissner-Nordstr$\ddot{o}$m metric.

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.

A new well behaved class of charge analogue of Adler’s relativistic exact solution

The paper presents a new class of parametric interior solutions of Einstein-Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged perfect fluid with a particular form of electric field intensity. This solution gives us wide range of parameter, K, for which the solution is well behaved hence, suitable for modeling of superdense star. For this solution the gravitational mass of a superdense object is maximized with all degree of suitability by assuming the surface density of the star equal to the normal nuclear density 2.5E17 kg/m3. By this model we obtain the mass of the Crab pulsar 1.401 Solar mass and the radius 12.98 km constraining the moment of inertia parameter greater than 1.61 for the conservative estimate of Crab nebula mass 2 Solar mass and 2.0156 Solar mass with radius 14.07 km constraining the moment of inertia parameter greater than 3.04 for the newest estimate of Crab nebula mass 4.6 Solar mass which are quite well in agreement with the possible values of mass and radius of Crab pulsar.Besides this, our model yields the moments of inertia for PSR J0737-3039A and PSR J0737-3039B are 1.4624E38 kgm2 and 1.2689E38 kgm2 respectively. It has been observed that under well behaved conditions this class of parametric solution gives us the maximum gravitational mass of causal superdense object 2.8020 Solar mass with radius 14.49 km, surface redshift 0.4319, charge 4.67E20 C, and central density 2.68 times nuclear density.

New class of Well behaved exact solutions of relativistic charged white-dwarf star with perfect fluid

The paper presents a class of interior solutions of Einstein-Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid. This class of solutions describes well behaved charged fluid balls. The class of solutions gives us wide range of parameter K (0.3277≤K≤0.49), for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρb=2×1014 g/cm3. Corresponding to K=0.3277 with X=−0.15, the maximum mass of the star comes out to be M=0.92MΘ with radius rb≈17.15 km and the surface red shift Zb≈0.087187. It has been observed that under well behaved conditions this class of solutions gives us the mass of super dense object within the range of white-dwarf.

Charged analogue of Vlasenko-Pronin superdense star in general relativity

In this article we have derived a set of three static spherical symmetric well behaved solutions of Einstein-Maxwell field equations is obtained for a specific choice of electric field involving a parameter K. The solutions so obtained can be seen as a charge analogue of the neutral solution due to Vlasenko and Pronin. The physical features of solutions so obtained and that of Vlasenko and Pronin are investigated subject to the reality and the causality conditions i.e. Pressure, density (greater than pressure), pressure-density ratio and velocity of sound (less than the velocity of light) are positive and monotonically decreasing and the electric intensity is monotonically increasing in nature away from the centre. The maximum mass and radius occupied by the neutral solution are 2.1434 MΘ and 16.7300 km respectively. For the charged solution, overall maximum mass and corresponding radius are found to be 6.8714 MΘ and 20.6166 km respectively (for K=1.343).

Well Behaved Parametric Class of Exact Solutions of Einstein-Maxwell Field Equations in General Relativity

We present a new well behaved class of exact solutions of Einstein-Maxwell field equations. This solution describes charge 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 gravitational red shift is positive throughout positive within the ball. Outmarch of pressure, density, pressure-density ratio, the adiabatic speed of sound and gravitational red shift is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. The solution gives us wide range of parameter K (0.72 ≤ K ≤ 2.41) for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρb = 2 × 1014g/cm3. Corresponding to K = 0.72 with X = 0.15, the resulting well behaved model has the mass M = 1.94 MΘ with radius rb » 15.2 km and for K = 2.41 with X = 0.15, the resulting well behaved model has the mass M = 2.26 MΘ with radius rb » 14.65 km.

Higher dimensional exact solutions for a charged fluid sphere in general theory of relativity

The exact higher dimensional solutions of Einstein-Maxwell field equations for spherically symmetric distribution of charged perfect fluid are obtained by using the method originally used by Hajj-Boutros and Sfeila (Gen. Relativ. Gravit. 18(4):395, 1986) for four-dimensional space-time. The new exact solutions have been generated from those of Khadekar et al. (J. Indian Math. Soc. 68(1–4):33, 2001), Humi and Mansour (Phys. Rev. D 29(6):1076, 1984) and Banerjee and Santos (J. Math. Phys. 22(4):824, 1981) in the frame work of higher dimensional space-time. The various physical properties are also discussed.

Realistic exact solution for the exterior field of a rotating neutron star

A new six-parametric, axisymmetric, and asymptotically flat exact solution of Einstein-Maxwell field equations having reflection symmetry is presented. It has arbitrary physical parameters of mass, angular momentum, mass-quadrupole moment, current octupole moment, electric charge, and magnetic dipole, so it can represent the exterior field of a rotating, deformed, magnetized, and charged object; some properties of the closed-form analytic solution such as its multipolar structure, electromagnetic fields, and singularities are also presented. In the vacuum case, this analytic solution is matched to some numerical interior solutions representing neutron stars, calculated by Berti and Stergioulas [E. Berti and N. Stergioulas, Mon. Not. R. Astron. Soc. 350, 1416 (2004)], imposing that the multipole moments be the same. As an independent test of accuracy of the solution to describe exterior fields of neutron stars, we present an extensive comparison of the radii of innermost stable circular orbits (ISCOs) obtained from the Berti and Stergioulas numerical solutions, the Kerr solution [R. P. Kerr, Phys. Rev. Lett. 11, 237 (1963)], the Hartle and Thorne solution [J. B. Hartle and K. S. Thorne, Astrophys. J. 153, 807 (1968)], an analytic series expansion derived by Shibata and Sasaki [M. Shibata and M. Sasaki, Phys. Rev. D 58, 104011 (1998)], and our exact solution. We found that radii of ISCOs from our solution fits better than others with realistic numerical interior solutions.

Solutions of Einstein-Maxwell field equations

A generalization of the Weyl solutions of coupled Einstein-Maxwell field equations is obtained and corresponding to a unique requirement on the potential the space-time metric is transformed into the isotropic form.

Exact Solutions for Shear-free Motion of Spherically Symmetric Charged Perfect Fluid Distributions in General Relativity

An in-depth study of various methods, and their correlations, of obtaining exact solutions of Einstein-Maxwell field equations representing shear free motion of spherically symmetric charged perfect fluid distributions has been made. It is shown that one can employ isotropic coordinate systems without any loss of generality. However the investigations have been carried out in an arbitrary coordinate system. The exact solutions relating to simple situations viz. (i) homogeneous density distribution, ϱ=ϱ(t), (ii) conformally flat solutions and (iii) distributions obeying an equation of state, p=p(ϱ) are briefly discussed. The methods due to MCVITTIE (1967), introduced initially for neutral fluids, and MASHHON and PARTOVI (1979) where one assumes the metric in a convenient form form one group and the methods due to SHAH and VAIDYA (1968), CHAKRAVARTY and CHATTERJEE (1978), CHATTERJEE (1984) and SUSSMAN (1987) where one chooses suitably two arbitrary functions of integration form the other group. This splitting of various methods into two is based on the earlier analogous work for the neutral fluids due to SRIVASTAVA (1987). Using McVittie's procedure we obtain a solution which in its uncharged limit reduces to Friedmann-Robertson-Walker solution whereas for non-vanishing charge is equivalent to the solution due to SHAH and VAIDYA (1967). This solution is termed as generalised Shah-Vaidya solution or charged Friedmann-Robertson-Walker solution. A suitable generalisation of Mashhoon and Partovi's procedure has been found to contain MASHHOON-PARTOVI solution (1979) and SHAH-VAIDYA solution (1967) as members of a class. The method employed by CHATTERJEE (1978), which does not yield the general solution of the problem, has been shown to lead to the procedure adopted by SUSSMAN (1987) after it is generalised suitably. The McVittie type and Wyman type solutions introduced by Sussman has been found to be contained in McV class of metries discussed here. It is also found that solutions obtained by CHAKRAVARTY and CHATTERJEE (1978) represent a class of charged Kustaanheimo-Qvist solution which are expressible as elementary functions. Finally, all known solutions have been derived introducing an adhoc assumption in the form of a mathematical relation and searching for the solutions free from movable critical points.

Imparting inhomogeneity to Bianchi type II, VIII and IX space-times with electromagnetic field

A unified treatment of Bianchi type II, VIII and IX space-times is given. A general scheme of imparting inhomogeneity to such space-time is developed. Exact solutions of Einstein-Maxwell field equations with Bianchi II, VIII and IX symmetrics are derived. The solutions describe the gravitational fields of a mass particle embedded in Bianchi type II, VIII and IX universes with electromagnetic fields. The details of the solutions are also discussed.

Radiating Demianski-type metrics and the Einstein-Maxwell fields

AbstractA Demianski-type metric is investigated in connection with the Einstein-Maxwell fields. Using complex vectorial formalism, some exact solutions of Einstein-Maxwell field equations for source-free electromagnetic fields plus pure radiation fields are obtained. The radiating Demianski solution, the Debney-Kerr-Schild solution and the Brill solution are derived as particular cases.

Generalised Kerr-Schild transformation from vacuum backgrounds to Einstein-Maxwell spacetimes

The generalised Kerr-Schild transformation on a vacuum background is used to generate exact solutions of Einstein-Maxwell field equations. Two families of algebraically general solutions are obtained. For generic values of a certain parameter a, they consist of the homogeneous non-static metrics given by Datta (1965). For a=1+or-2, there are solutions with only two commuting spacelike Killing vectors.

Kerr-Newman metric in deSitter background

In addition to the Kerr-Newman metric with cosmological constant several other metrics are presented giving Kerr-Newman type solutions of Einstein-Maxwell field equations in the background of deSitter universe. The electromagnetic field in all the solutions is assumed to be source-free. A new metric of what may be termed as an electrovac rotating de-Sitter space-time—a space-time devoid of matter but containing source-free electromagnetic field and a null fluid with twisting rays—has been presented. In the absence of the electromagnetic field, our solutions reduce to those discussed by Vaidya.