Charged Perfect Fluid Research Articles

Charged perfect fluid dark matter model: Known mass density function approach

The concept of dark matter has been imported to explain the observed velocity profile of the spiral galaxies, the flat rotational velocity. Taking the flatness of rotation curves as an input and assuming that the galactic halo is filled with charged perfect fluid having known mass density function, we obtain a space time metric in the galactic halo region. The acquired solution indicates to a (nearly) flat universe, consistent with the present day cosmological observations. Various other aspects of the solution such as attractive gravity in the halo region, stability of the circular orbit, etc., are also analyzed.

A simple geometry to model fluid spheres in general relativity

A simple geometry which is static and spherically symmetrical is proposed, useful to model a fluid sphere in general relativity. This allows us to describe the interior of stellar objects both neutral and charged. It is shown that in both cases the solution is stable, which means that the behavior of the density and radial pressure is monotonic decreasing functions. Both models depend on two parameters, in the neutral case, these are the compactness rate $$u=GM/c^2R$$ and w related to the monotonically increasing or decreasing behavior of the speed of sound, and in the charged case, they are the compactness rate and the rate between the charge Q and the radius R, $$q=Q/R$$ . A comparison is done between the case of a charged perfect fluid and the case of an anisotropic fluid; from there we can show that, as a result of the presence of the charge and its repulsion effect that it generates at a local and universal level, the density for the anisotropic case is greater than the density in the charged case. For both models, we obtain physical values of objects with a compactness rate $$u=0.35578$$ for the particular cases of masses and radios for $$(M_\odot ,R=4150.1\,\mathrm{m})$$ , $$(1.5M_\odot ,R=6225\,\mathrm{m})$$ , $$(2M_\odot ,R=8300 m)$$ . In the neutral case, the greater central density $$\rho _c=5.0840\times 10^{19} \,\mathrm{kg/m}^3$$ matches the object of $$1.5M_\odot $$ and for the charged case, the maximum central density is of $$\rho _c=8.8439\times 10^{18} \,\mathrm{kg/m}^3$$ , associated with the star with $$1M_\odot $$ . Additionally, by using the proposed model, we obtain the values of density and pressure for the star PSR J1614–223, the maximum value of the central density $$\rho _c=1.0573\times 10^{18} \,\mathrm{kg/m}^3$$ .

Nonsingular black holes from charged dust collapse: A concrete mechanism to evade interior singularities in general relativity

In this paper, we examine the gravitational collapse of a nonrelativistic charged perfect fluid interacting with a dark energy component. Given a simple factor for the energy transfer, we obtain a nonsingular interior solution which naturally matches the Reissner–Nordström–de Sitter exterior geometry. We also show that the interacting parameter is proportional to the overall charge of the final black hole thus formed. For the case of quasi-extremal configurations, we propose a statistical model for the entropy of the collapsed matter. This entropy extends Bekenstein’s geometrical entropy by an additive constant proportional to the area of the extremal black hole.

Charged perfect fluid stellar structures with Bardeen model

This paper is devoted to study static spherically symmetric model in the presence of charged perfect fluid. This is the generalization of neutral perfect fluid (when there is no charge) through the solution of Einstein Maxwell equations. For this purpose, we consider a suitable form of gravitational potential [Formula: see text] and the electric field [Formula: see text], already used in the literature. The value of mass-radius ratio or compactness [Formula: see text], which depends upon the chosen model exceeds the value [Formula: see text] corresponding to neutral stars. The most important feature of the current study is to use the Bardeen model geometry instead of usual Reissner–Nordström model for the matching conditions. In this case the energy density and pressure remain positive, bounded and monotonically decreasing whereas electric field is monotonically increasing. Also the causality condition, i.e. the magnitude of speed of sound must be less than the speed of light, is satisfied. Moreover, the behavior of all the physical parameters at the center and on surface of star of mass [Formula: see text] and for Her X-1 are tabulated. All the results by graphical analysis and tabular information suggest that Bardeen model provides physically realistic stellar structures.

Study of the charged super-Chandrasekhar limiting mass white dwarfs in the f(R,T) gravity

The equilibrium configuration of white dwarfs composed of a charged perfect fluid are investigated in the context of the $f(R,\mathcal{T})$ gravity, for which $R$ and $\mathcal{T}$ stand for the Ricci scalar and the trace of the energy-momentum tensor, respectively. By considering the functional form $f(R, \mathcal{T})=R+2\chi \mathcal{T}$, where $\chi$ is the matter-geometry coupling constant, and for a Gaussian ansatz for the electric distribution, some physical properties of charged white dwarfs were derived, namely: mass, radius, charge, electric field, effective pressure and energy density; their dependence on the parameter $\chi$ was also derived. In particular, the $\chi$ value important for the equilibrium configurations of charged white dwarfs has the same scale of $10^{-4}$ of that for non-charged stars and the order of the charge was $10^{20}$C, which is scales with the value of one solar mass, i.e., $\sqrt{G}M_\odot\sim 10^{20}$C. We have also shown that charged white dwarf stars in the context of the $f(R,\mathcal{T})$ have surface electric fields generally below the Schwinger limit of $1.3\times 10^{18}$V/m. In particular, a striking feature of the coupling between the effects of charge and $f(R,\mathcal{T})$ gravity theory is that the modifications in the background gravity increase the stellar radius, which in turn diminishes the surface electric field, thus enhancing stellar stability of charged stars. Most importantly, our study reveals that the present $f(R,T)$ gravity model can suitably explain the super-Chandrasekhar limiting mass white dwarfs, which are supposed to be the reason behind the over-luminous SNeIa and remain mostly unexplained in the background of general relativity (GR).

A charged perfect fluid solution

A static and spherically symmetric stellar model is described by a perfect charged fluid. Its construction is done using the solution of the Einstein–Maxwell equations for which we specify the temporal metric and the electric field which is a monotonic increasing function null in the center. The density, pressure and speed of sound turn out to be regular functions, positive and monotonic decreasing as function of the radial distance. Also, the speed of sound is lower than the speed of light, that is to say, it does not violate the condition of causality. The value of compactness [Formula: see text], so the model is useful to represent neutron stars of quark stars. In a complementary manner, we report the physical values when describing a star of mass [Formula: see text] and radius [Formula: see text], in such case [Formula: see text], and given the presence of the charge, the interval for the central density [Formula: see text].

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.

Charged perfect fluid sphere in higher-dimensional spacetime

In the present paper, a new model for perfect fluid sphere filled with charge, in higher-dimensional spacetime, admitting conformal symmetry has been investigated. We have considered a linear equation of state, with coefficients fixed by the matching conditions, at the boundary of the source corresponding to the exterior Reissner–Nordström higher-dimensional spacetime. Several physical features for different dimensions, starting from four up to eleven, have been briefly discussed. It has been shown that all the features as obtained from the present model are physically desirable.

New classes of spherically symmetric, inhomogeneous cosmological models

We present two classes of inhomogeneous, spherically symmetric solutions of the Einstein-Maxwell-Perfect Fluid field equations with cosmological constant generalizing the Vaidya-Shah solution. Some special limits of our solution reduce to the known inhomogeneous charged perfect fluid solutions of the Einstein field equations and under some other limits we obtain new charged and uncharged solutions with cosmological constant. Uncharged solutions in particular represent cosmological models where the universe may undergo a topology change and in between is a mixture of two different Friedmann-Robertson-Walker universes with different spatial curvatures. We show that there exist some spacelike surfaces where the Ricci scalar and pressure of the fluid diverge but the mass density of the fluid distribution remains finite. Such spacelike surfaces are known as (sudden) cosmological singularities. We study the behavior of our new solutions in their general form as the radial distance goes to zero and infinity. Finally, we briefly address the null geodesics and apparent horizons associated to the obtained solutions.

Dynamically equivalent Λ CDM equations with underlying Bianchi Type geometry

Solutions have been found for gravity coupled to electromagnetic field and a set of charged and uncharged perfect fluids for Bianchi Types VI(−1), VIII, IX. It has been assumed that the anisotropy is “frozen”, γμν=α(t)2mμν, where γμν and mμν are the spatial metric and some constant matrix respectively. This, according to previous works, results in the existence of a conformal Killing vector field proportional to the fluid velocity of the comoving matter, which guarantees the absence of parallax effects and the independence of the temperature (assuming black body spectrum) from the direction of observation. The electromagnetic field “absorbs” the “frozen” anisotropy and the remaining equations are dynamically equivalent with the equations of Λ CDM. There are solutions with flat, negative and positive effective spatial curvature corresponding to the three FLRW classes. Three equations of state for the charged perfect fluid were studied: non-relativistic w=0, relativistic w=1/3 and dark energy-like w=−1. For the first two cases, maximum values exist for the scale factor, in order for the weak energy conditions to be respected, which depend upon the geometric and charged fluid parameters. A minimum value for the scale factor exists (for the solutions to be valid) in all the cases and Types, indicating the absence of initial spacetime singularity (big bang). This minimum value depends upon the geometric and electromagnetic parameters. The number of essential constants in the final form of each metric is the minimum without loss of generality due to the use of the constant Automorphism's group. A known solution, with the anisotropy absorbed via one free scalar field is reproduced with our method and contains the minimum possible number of parameters.

A charged perfect fluid model with high compactness

A relativistic, static and spherically symmetrical stellar model is presented, constituted by a perfect charged fluid. This represents a generalization to the case of a perfect neutral fluid, whose construction is made through the solution to the Einstein-Maxwell equations proposing a form of gravitational potential $g_{tt}$ and the electric field. The choice of electric field implies that this model supports values of compactness$u=GM/c^2R\leq 0.5337972212$, values higher than the case without electric charge ($u\leq 0.3581350065$), being this feature of relevance to get to represent compact stars. In addition, density and pressure are positive functions, bounded and decreasing monotones, the electric field is a monotonously increasing function as well as satisfying the condition of causality so the model is physically acceptable. In a complementary way, the internal behavior of the hydrostatic functions and their values are obtained taking as a data the corresponding to a star of $1 M_\odot$,for different values of the charge parameter, obtaining an interval for the central density $\rho_c\approx (7.9545,2.7279) 10^{19}$ $ Kg/m^3$ characteristic of compact stars.

Charged perfect fluid gravitational collapse in f(R, T) gravity

We explore the problem of charged perfect fluid spherically symmetric gravitational collapse in f(R, T) gravity (R is Ricci scalar and T is the trace of energy–momentum tensor). We have taken the interior boundary of a star as spherically symmetric metric filled with the charged perfect fluid. In order to study charged perfect fluid collapse, we have investigated the exact solutions of the Maxwell–Einstein field equations solutions using the most simplified form for f(R, T) model f(R, T) = R + 2[Formula: see text]T, where [Formula: see text] is model parameter. This study involves the effects of charge as well as coupling parameter on collapse of a star. We studied the nature of trapped surfaces, apparent horizon and singularity structure in detail. It has been found that singularity is formed earlier than the apparent horizons, so the end state of gravitational collapse in this case is black hole.

Relativistic disks with two charged perfect fluids components

A method to describe exact solutions of the Einstein-Maxwell field equations in terms of relativistic thin disks constituted by two perfect charged fluids is presented. Describing the surface of the disk as a single charged fluid we find explicit expressions for the rest energies, the pressures and the electric charge densities of the two fluids. An explicit example is given. The particular case of the thin disks composed by two charged perfect fluids with barotropic equation of state is also presented.

Study of charged spherical collapse in $f(\mathcal{G},T)$ f ( 𝒢 , T ) gravity

This paper deals with the dynamics of charged spherical perfect fluid collapse in the framework of $f(\mathcal{G},T)$ gravity. We formulate dynamical equations through the Misner-Sharp formalism and investigate the effects of correction terms, fluid parameters as well as electromagnetic field on the collapse rate. We also construct a relationship among Weyl scalar, correction terms, electric field intensity and energy density. For zero electric charge and constant $f(\mathcal{G},T)$ , it is found that if the metric is conformally flat then energy density is homogeneous and vice versa. We conclude that the electric charge and positive correction terms behave as anti-gravitational force and hence diminish the collapse rate.

The Solutions of the Coupled Einstein-Maxwell Equations and Dilaton Equations

In this paper, we consider extremely charged static perfect fluid distributions with a dilaton field in the framework of general relativity. By using calculus of variations, we establish the existence theorem for the solutions of this important gravitational system. We show that there is a continuous family of smooth solutions realizing asymptotically flat space metrics.

Higher-dimensional charged LTB collapse in f(R) gravity

This paper deals with the study of the gravitational collapse of a charged perfect fluid in n+2 dimensions in f(R) gravity. The Darmois matching criterion is used to formulate the junction conditions between the Lemaitre-Tolman-Bondi metric (interior) and Reissner-Nordstrom metric (exterior) in n+2 dimensions while Senovilla junction conditions for f(R) gravity are also considered. The field equations are solved for the constant curvature which implies that matter variables are constant quantities. The expression for the time difference between the formation of trapped surfaces and singularity is established which supports the cosmic censorship hypothesis. We conclude that the electromagnetic field affects this time difference by reducing the repulsive effect of f R0) term. It is also found that the collapse rate of the charged fluid is faster as compared to the perfect fluid.

Weakly charged compact stars in f(R) gravity

We study electrically charged compact stars in the framework of one class of the extended theories of gravity (ETG), namely the f(R) gravity theory. We assume that the charge density is proportional to the energy density. The polytropic equation of state is chosen to describe the state of the charged perfect fluid. We aim to find the Oppenheimer Volkoff (OV) mass limit for charged compact stars. A detailed numerical study is performed. We show the dependence of the mass-radius diagram of the spheres on the values of the small parameter β, the polytropic exponent γ and the charge fraction α. Our results are compared with those found in the literature in the case of applying General Relativity (GR).

Equilibrium configurations of a charged fluid around a Kerr black hole

Equilibrium configurations of electrically charged perfect fluid surrounding a central rotating black hole endowed with a test electric charge and embedded in a large-scale asymptotically uniform magnetic field are presented. Following our previous studies considering the central black hole non-rotating, we show that in the rotating case, conditions for the configurations existence change according to the spin of the black hole. We focus our attention on the charged fluid in rigid rotation which can form toroidal configurations centered in the equatorial plane or the ones hovering above the black hole, along the symmetry axis. We conclude that a non-zero value of spin changes the existence conditions and the morphology of the solutions significantly. In the case of fast rotation, the morphology of the structures is close to an oblate shape.

White dwarfs with a surface electrical charge distribution: equilibrium and stability

The equilibrium configuration and the radial stability of white dwarfs composed of charged perfect fluid are investigated. These cases are analyzed through the results obtained from the solution of the hydrostatic equilibrium equation. We regard that the fluid pressure and the fluid energy density follow the relation of a fully degenerate electron gas. For the electric charge distribution in the object, we consider that it is centralized only close to the white dwarfs’ surfaces. We obtain larger and more massive white dwarfs when the total electric charge is increased. To appreciate the effects of the electric charge in the structure of the star, we found that it must be in the order of 10^{20},[mathrm{C}] with which the electric field is about 10^{16},[mathrm{V/cm}]. For white dwarfs with electric fields close to the Schwinger limit, we obtain masses around 2,M_{odot }. We also found that in a system constituted by charged static equilibrium configurations, the maximum mass point found on it marks the onset of the instability. This indicates that the necessary and sufficient conditions to recognize regions constituted by stable and unstable equilibrium configurations against small radial perturbations are respectively dM/drho _c>0 and dM/drho _c<0.

On some structure results for Gödel-type spacetimes

In this paper, we prove structure results on Gödel-type spacetimes, which we understand as stationary charged perfect fluid solutions of the Einstein–Maxwell equations with geodesic flow. Given in a standard product form, we investigate relations between the vorticity and the geometry of the fiber. For the four dimensional case in particular, we classify the Gödel-type spacetimes with constant vorticity scalar. We give a complete list of the solutions, which provides a generalization of an observation by Gödel, proved later by Ozsváth: The Gödel spacetime and Einstein’s static universe are the only stationary Λ -dust solutions of Einstein’s equations with positive energy density that are spatially homogeneous.