Relativistic Charged Spheres Research Articles

Relativistic charged sphere in f(G,T) gravity

This study explores the interior geometry of static relativistic charged spheres in the background of a recently proposed modified [Formula: see text] gravity, where [Formula: see text] and [Formula: see text] are the Gauss–Bonnet (GB) invariant and trace of energy–momentum tensor, respectively. The GB gravity is the low-energy limit of superstring theories. The structures of specific relativistic charged spheres Vela [Formula: see text], [Formula: see text], and [Formula: see text] are studied in this theory of gravity. We analyzed several physical behaviors of these relativistic charged spheres with the help of observational data and investigated the various aspects like density profile, stresses, the distribution of charges, stability, etc.

An electromagnetic extension of the Schwarzschild interior solution and the corresponding Buchdahl limit

We wish to construct a model for charged star as a generalization of the uniform density Schwarzschild interior solution. We employ the Vaidya and Tikekar ansatz (Astrophys Astron 3:325, 1982) for one of the metric potentials and electric field is chosen in such a way that when it is switched off the metric reduces to the Schwarzschild. This relates charge distribution to the Vaidya–Tikekar parameter, k, indicating deviation from sphericity of three dimensional space when embedded into four dimensional Euclidean space. The model is examined against all the physical conditions required for a relativistic charged fluid sphere as an interior to a charged star. We also obtain and discuss charged analogue of the Buchdahl compactness bound.

Publisher’s Note: Plethora of relativistic charged spheres: The full spectrum of Guilfoyle’s static, electrically charged spherical solutions [Phys. Rev. D 95 , 104040 (2017)

Publisher’s Note: Plethora of relativistic charged spheres: The full spectrum of Guilfoyle’s static, electrically charged spherical solutions [Phys. Rev. D <b>95</b> , 104040 (2017)

General Relativistic Charged Dust Sphere with Conformal Flatness

General Relativistic Charged Dust Sphere with Conformal Flatness

Relativistic charged spheres: compact stars, compactness and stable configurations

This paper aims to explore a class of static stellar equilibrium configuration of relativistic charged spheres made of a charged perfect fluid. For solving the Einstein-Maxwell field equations, we consider a particularized metric potential, Buchdahl ansatz [1] and then by using a simple transformation. The study is developed by matching the interior region with Riessner-Nordström metric as an exterior solution. The matter content the charged sphere satisfies all the energy conditions and hydrostatic equilibrium equation, i.e. the modified Tolman-Oppenheimer-Volkoff (TOV) equation for the charged case is maintained. In addition to this, we also discuss some important properties of the charged sphere such as total electric charge, mass-radius relation, surface redshift, and the speed of sound. Obtained solutions are presented by the graphical representation that provides strong evidence for a more realistic and viable stellar structure. Obtained results are compared with analogue objects with similar mass and radii, such as SAX J1808.4-3658, 4U 1538-52, PSR J1903+327, Vela X-1, and 4U1608-52. It is also noted that the Buchdahl ansatz for a given transformation provides a physically viable solution only for the charged case when 0 < K < 1, where density and pressure are maximum at the center and monotonically decreasing towards the boundary. Obtained results are also quite important both from theoretical and astrophysical scale to analyze other compact objects such as white dwarfs, neutron stars, boson stars, and quark stars.

Comparison among three types of relativistic charged anisotropic fluid spheres for self-bound stars

The number of exact solutions for spherically symmetric anisotropic fluid spheres is derived. And the relativistic model of an electrically charged compact star whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself, such as electrically charged bare strange stars is also investigated. Among the three models, Heintzmann and Durgapal IV, and V permit a simple method that provide bounds on the maximum possible mass of compact electrically charged self-bound stars, and numerically exhibit that the maximum compactness and mass increase in the presence of an electric field and anisotropic pressure. Based on analytic models developed in this work, it has been compared to investigate which one is better than the others; the values of some pertinent physical quantities have been considered by assuming the estimated masses and radii of some well-known potential strange star candidates like Vela X-1, Cen X-3, PSR J1903+327 and EXO 1785-248. This analysis depends on several mathematical assumptions.

A family of solutions to the Einstein–Maxwell system of equations describing relativistic charged fluid spheres

In this paper, we present a formalism to generate a family of interior solutions to the Einstein–Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner–Nordström space–time. By reducing the Einstein–Maxwell system to a recurrence relation with variable rational coefficients, we show that it is possible to obtain closed-form solutions for a specific range of model parameters. A large class of solutions obtained previously are shown to be contained in our general class of solutions. We also analyse the physical viability of our new class of solutions.

Plethora of relativistic charged spheres: The full spectrum of Guifoyle’s static, electrically charged spherical solutions

We show that Guilfoyle's exact solutions of the Einstein-Maxwell equations for spherical symmetric static electrically charged matter with a Reissner-Nordstr\"om exterior possess a bewildering plethora of different types of solutions. For the parameter space of the solutions we use two normalized variables, $q^2/R^2$ and $r_0/R$, where $q$ is the total electric charge, $r_0$ is the radius of the object, and $R$ is a length representing the square root of the inverse energy density of the matter. The two other parameters, the mass $m$ and the Guilfoyle parameter $a$, both dependent on $q$, $r_0$ and $R$, are analyzed in detail. The full parameter space of solutions $q^2/R^2\times r_0/R$ is explored with the corresponding types of solutions being identified and analyzed. The different types of solutions are regular charged stars, including charged dust stars and stars saturating the Buchdahl-Andr\'easson bound, quasiblack holes, regular charged black holes with a de Sitter core, regular black holes with a core of phantom charged matter, other exotic regular black holes, Schwarzschild stars, Schwarzschild black holes, Kasner spacetimes, pointlike and planar naked singularities, and the Minkowski spacetime. Allowing for $q^2<0$, in which case it is not possible to interpret $q$ as electric charge, also yields new solutions, some of which are interesting and regular, others are singular. Some of these types of solutions as well as the matter properties have been previously found and studied, here the full spectrum being presented in a unified manner.

Some new Wyman–Leibovitz–Adler type static relativistic charged anisotropic fluid spheres compatible to self-bound stellar modeling

In this work some families of relativistic anisotropic charged fluid spheres have been obtained by solving the Einstein–Maxwell field equations with a preferred form of one of the metric potentials, and suitable forms of electric charge distribution and pressure anisotropy functions. The resulting equation of state (EOS) of the matter distribution has been obtained. Physical analysis shows that the relativistic stellar structure for the matter distribution considered in this work may reasonably model an electrically charged compact star whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself (e.g., electrically charged bare strange stars). Furthermore these models permit a simple method of systematically fixing bounds on the maximum possible mass of cold compact electrically charged self-bound stars. It has been demonstrated, numerically, that the maximum compactness and mass increase in the presence of an electric field and anisotropic pressures. Based on the analytic models developed in this present work, the values of some relevant physical quantities have been calculated by assuming the estimated masses and radii of some well-known potential strange star candidates like PSR J1614-2230, PSR J1903+327, Vela X-1, and 4U 1820-30.

Sharp bounds on the radius of relativistic charged spheres: Guilfoyle's stars saturate the Buchdahl–Andréasson bound

Buchdahl, by imposing a few reasonable physical assumptions on matter, i.e., its density is a nonincreasing function of the radius and the fluid is a perfect fluid, and on the configuration, such as the exterior is the Schwarzschild solution, found that the radius r0 to mass m ratio of a star would obey the bound , the Buchdahl bound. He also noted that the bound was saturated by the Schwarzschild interior solution, i.e., the solution with , where is the energy density of the matter at r, when the central central pressure blows to infinity. Generalizations of this bound in various forms have been studied. An important generalization was given by Andréasson, by including electrically charged matter and imposing a different set of conditions, namely, , where p is the radial pressure and pT the tangential pressure. His bound is sharp and given by , the Buchdahl–Andréasson bound, with q being the total electric charge of the star. For q = 0 one recovers the Buchdahl bound. However, following Andréasson's proof, the configuration that saturates the Buchdahl bound is an uncharged shell, rather than the Schwarzschild interior solution. By extension, the configurations that saturate the electrically charged Buchdahl–Andréasson bound are charged shells. One could expect then, in turn, that there should exist an electrically charged equivalent to the interior Schwarzschild limit. We find here that this equivalent is provided by the equation , where is the electric charge at r. This equation was put forward by Cooperstock and de la Cruz, and Florides, and realized in Guilfoyle's stars. When the central pressure goes to infinity, Guilfoyle's stars are configurations that also saturate the Buchdahl–Andréasson bound. A proof in Buchdahl's manner, such that these configurations are the limiting configurations of the bound, remains to be found.

Some static relativistic compact charged fluid spheres in general relativity

In this work a new family of relativistic models of electrically charged compact star has been obtained by solving Einstein–Maxwell field equations with preferred form of one of the metric potentials and a suitable form of electric charge distribution function. The resulting equation of state (EOS) has been calculated. The relativistic stellar structure for matter distribution obtained in this work may reasonably models an electrically charged compact star whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself (e.g. electrically charged bare strange stars). Based on the analytic model developed in the present work, the values of the relevant physical quantities have been calculated by assuming the estimated masses and radii of some well known strange star candidates like X-ray pulsar Her X-1, millisecond X-ray pulsar SAX J 1808.4-3658, and 4U 1820-30.

A new family of polynomial solutions for charged fluid spheres

We present a new family of relativistic charged fluid spheres described by a space time metric with a prescribed metric potential g 44 along with the specific choice of electric field intensity which vanishes at the centre and monotonically increasing towards the pressure free surface. The charged fluid solutions so obtained satisfy all the energy conditions along with the velocity of sound which decreases away from the centre. Also the solutions are utilized to construct the models of super-dense stars.

Variety of Well behaved parametric classes of relativistic charged fluid spheres in general relativity

The paper presents a variety of classes of interior solutions of Einstein–Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid with well behaved nature. These classes of 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 center. 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, two new classes of solutions are being studied extensively. Moreover, these classes of solutions give us wide range of constant K for which the solutions are well behaved hence, suitable for modeling of super dense star. For solution (I1) 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=1.19 and X=0.20, the maximum mass of the star comes out to be 2.5MΘ with linear dimension 25.29 Km and central redshift 0.2802. It has been observed that with the increase of charge parameter K, the mass of the star also increases. For n=4,5,6,7, the charged solutions are well behaved with their neutral counterparts however, for n=1,2,3, the charged solution are well behaved but their neutral counterparts are not well behaved.

Quasiblack holes with pressure: Relativistic charged spheres as the frozen stars

In general relativity coupled to Maxwell's electromagnetism and charged matter, when the gravitational potential $W^2$ and the electric potential field $\phi$ obey a relation of the form $W^{2}= a\left(-\epsilon\, \phi+ b\right)^2 +c$, where $a$, $b$ and $c$ are arbitrary constants, and $\epsilon=\pm1$ (the speed of light $c$ and Newton's constant $G$ are put to one), a class of very interesting electrically charged systems with pressure arises. We call the relation above between $W$ and $\phi$, the Weyl-Guilfoyle relation, and it generalizes the usual Weyl relation, for which $a=1$. For both, Weyl and Weyl-Guilfoyle relations, the electrically charged fluid, if present, may have nonzero pressure. Fluids obeying the Weyl-Guilfoyle relation are called Weyl-Guilfoyle fluids. These fluids, under the assumption of spherical symmetry, exhibit solutions which can be matched to the electrovacuum Reissner-Nordstr\"om spacetime to yield global asymptotically flat cold charged stars. We show that a particular spherically symmetric class of stars found by Guilfoyle has a well-behaved limit which corresponds to an extremal Reissner-Nordstr\"om quasiblack hole with pressure, i.e., in which the fluid inside the quasihorizon has electric charge and pressure, and the geometry outside the quasihorizon is given by the extremal Reissner-Nordstr\"om metric. The main physical properties of such charged stars and quasiblack holes with pressure are analyzed. An important development provided by these stars and quasiblack holes is that without pressure the solutions, Majumdar-Papapetrou solutions, are unstable to kinetic perturbations. Solutions with pressure may avoid this instability. If stable, these cold quasiblack holes with pressure, i.e., these compact relativistic charged spheres, are really frozen stars.

Conformal anisotropic relativistic charged fluid spheres with a linear equation of state

We obtain two new families of compact solutions for a spherically symmetric distribution of matter consisting of an electrically charged anisotropic fluid sphere joined to the Reissner–Nordstrom static solution through a zero pressure surface. The static inner region also admits a one parameter group of conformal motions. First, to study the effect of the anisotropy in the sense of the pressures of the charged fluid, besides assuming a linear equation of state to hold for the fluid, we consider the tangential pressure p ⊥ to be proportional to the radial pressure p r , the proportionality factor C measuring the grade of anisotropy. We analyze the resulting charge distribution and the features of the obtained family of solutions. These families of solutions reproduce for the value C=1, the conformal isotropic solution for quark stars, previously obtained by Mak and Harko. The second family of solutions is obtained assuming the electrical charge inside the sphere to be a known function of the radial coordinate. The allowed values of the parameters pertained to these solutions are constrained by the physical conditions imposed. We study the effect of anisotropy in the allowed compactness ratios and in the values of the charge. The Glazer’s pulsation equation for isotropic charged spheres is extended to the case of anisotropic and charged fluid spheres in order to study the behavior of the solutions under linear adiabatic radial oscillations. These solutions could model some stage of the evolution of strange quark matter fluid stars.

Sharp bounds on the compactness of relativistic charged spheres

The problem of finding an upper bound on the mass M of a charged spherically symmetric static object with area radius R and charge Q < M is addressed. This problem has resulted in a number of papers in recent years but neither a transparent nor a general inequality similar to the case without charge, i.e., M ≤ 4R/9, has been found. Here, we discuss the surprisingly transparent inequality The inequality holds for any solution which satisfies p + 2pT ≤ ρ, where p ≥ 0 and pT are the radial- and tangential pressures respectively and ρ ≥ 0 is the energy density. Moreover, the inequality is sharp and in particular, sharpness holds for infinitely thin shell solutions.

Sharp Bounds on the Critical Stability Radius for Relativistic Charged Spheres

In a recent paper by Giuliani and Rothman \cite{GR}, the problem of finding a lower bound on the radius $R$ of a charged sphere with mass M and charge Q<M is addressed. Such a bound is referred to as the critical stability radius. Equivalently, it can be formulated as the problem of finding an upper bound on M for given radius and charge. This problem has resulted in a number of papers in recent years but neither a transparent nor a general inequality similar to the case without charge, i.e., M\leq 4R/9, has been found. In this paper we derive the surprisingly transparent inequality $$\sqrt{M}\leq\frac{\sqrt{R}}{3}+\sqrt{\frac{R}{9}+\frac{Q^2}{3R}}.$$ The inequality is shown to hold for any solution which satisfies $p+2p_T\leq\rho,$ where $p\geq 0$ and $p_T$ are the radial- and tangential pressures respectively and $\rho\geq 0$ is the energy density. In addition we show that the inequality is sharp, in particular we show that sharpness is attained by infinitely thin shell solutions.

Relativistic anisotropic charged fluid spheres with varying cosmological constant

Static spherically symmetric anisotropic source has been studied for the Einstein-Maxwell field equations assuming the erstwhile cosmological constant Λ to be a space-variable scalar, viz., Λ=Λ(r). Two cases are examined out of which one reduces to isotropic sphere. The solutions thus obtained are shown to be electromagnetic in origin as a particular case. It is also shown that the generally used pure charge condition, viz., ρ+p=0 is not always required for constructing electromagnetic mass models.

Absolute stability limit for relativistic charged spheres

We find an exact solution for the stability limit of relativistic charged spheres for the case of constant gravitational mass density and constant charge density. We argue that this provides an absolute stability limit for any relativistic charged sphere in which the gravitational mass density decreases with radius and the charge density increases with radius. We then provide a cruder absolute stability limit that applies to any charged sphere with a spherically symmetric mass and charge distribution. We give numerical results for all cases. In addition, we discuss the example of a neutral sphere surrounded by a thin, charged shell.

Instability of extremal relativistic charged spheres

With the question ``Can relativistic charged spheres form extremal black holes?'' in mind, we investigate the properties of such spheres from a classical point of view. The investigation is carried out numerically by integrating the Oppenheimer-Volkov equation for relativistic charged fluid spheres and finding interior Reissner-Nordstr\"om solutions for these objects. We consider both constant density and adiabatic equations of state, as well as several possible charge distributions, and examine stability by both a normal mode and an energy analysis. In all cases, the stability limit for these spheres lies between the extremal $(Q=M)$ limit and the black hole limit ${(R=R}_{+}).$ That is, we find that charged spheres undergo gravitational collapse before they reach $Q=M,$ suggesting that extremal Reissner-Nordstr\"om black holes produced by collapse are ruled out. A general proof of this statement would support a strong form of the cosmic censorship hypothesis, excluding not only stable naked singularities, but stable extremal black holes. The numerical results also indicate that although the interior mass-energy $m(R)$ obeys the usual $m/R&lt;4/9$ stability limit for the Schwarzschild interior solution, the gravitational mass M does not. Indeed, the stability limit approaches ${R}_{+}$ as $Q\ensuremath{\rightarrow}M.$ In the Appendix we also argue that Hawking radiation will not lead to an extremal Reissner-Nordstr\"om black hole. All our results are consistent with the third law of black hole dynamics, as currently understood.