Static Fluid Spheres Research Articles

Static Spherically Symmetric Anisotropic Fluid Distribution in Presence of Electromagnetic Field

Einstein’s field equations of general relativity corresponding to the anisotropic (principal stresses unequal) static fluid sphere in presence of electromagnetic field have been solved exactly. The integration constants are determined by matching the obtained solution with the Reissner-Nordstrom solution over the boundary. It has been found that the flaid model has non-negative expression for mass density and pressure. The mass density and stresses are everywhere regular and monotonically decreasing functions of the radial coordinate.

Static charged perfect fluid spheres in general relativity

Interior perfect fluid solutions for the Reissner-Nordstrom metric are studied on the basis of a new classification scheme. General formulas are found in many cases. Explicit new global solutions are given as illustrations. Known solutions are briefly reviewed.

Charged Static Fluid Spheres in General Relativity

The work is concerned with the charged analogue of Bayin's paper (1978) related to Tolman's type astrophysically interesting aspects of stellar structure.

Nonlocal equation of state in anisotropic static fluid spheres in general relativity

We show that it is possible to obtain, at least certain regions within spherically symmetric static matter configurations, credible anisotropic fluids satisfying a nonlocal equation of state. This particular type of equation of state provides, at a given point, the radial pressure not only as a function of the density at that point, but its functional throughout the enclosed distribution. To establish the physical plausibility of the proposed family of solutions satisfying a nonlocal equation of state, we study the constraints imposed by the junction, energy, and some intuitive physical conditions. We show that these static fluids having this particular equation of state are "naturally" anisotropic in the sense that they satisfy, identically, the anisotropic Tolman–Oppenheimer–Volkov equation. We also show that it is possible to obtain physically plausible static anisotropic spherically symmetric matter configurations starting from known density profiles, and also for configurations where tangential pressures vanish. This very particular type of relativistic sphere with vanishing tangential stresses is inspired by some of the models proposed to describe extremely magnetized neutron stars (magnetars) during the transverse quantum collapse.

Anisotropic charged fluid spheres in D space–time dimensions

The equations describing the hydrostatic equilibrium (mass continuity and Tolman–Oppenheimer–Volkoff) of a static anisotropic general relativistic fluid sphere are obtained in D (D⩾4) space–time dimensions in the presence of a cosmological constant. The formalism thus developed is used to study homogeneous anisotropic constant density charged fluid spheres and homogeneous anisotropic charged spheres with a neutral isotropic core in higher dimensions. For these configurations and with a particular choice of the proper charge density a complete solution of the coupled Einstein–Maxwell equations is obtained.

On most general exact solution for Vaidya-Tikekar isentropicsuperdense star

The energy density of Vaidya-Tikekar isentropic superdense star is found to be decreasing away from the center, only if the parameter K is negative. The most general exact solution for the star is derived for all negative values of K in terms of circular and inverse circular functions. Which can further be expressed in terms of algebraic functions for K = 2-(n/δ)2 < 0 (n being integer andδ = 1,2,3 4). The energy conditions 0 ≤ p ≤ αρc 2, (α = 1 or 1/3) and adiabatic sound speed conditiondp dρ ≤ c 2, when applied at the center and at the boundary, restricted the parameters K and α such that .18 < −K −2287 and.004 ≤ α ≤ .86. The maximum mass of the star satisfying the strong energy condition (SEC), (α = 1/3) is found to be3.82 Mq· at K=−2/3, while the same for the weak energy condition (WEC), (α =1) is 4.57 M_ ⊙ atK=−>5/2. In each case the surface density is assumed to be 2 × 1014 gm cm-3. The solutions corresponding to K>0 (in fact K>1) are also made meaningful by considering the hypersurfaces t= constant as 3-hyperboloid by replacing the parameter R 2 by −R2 in Vaidya-Tikekar formalism. The solutions for the later case are also expressible in terms of algebraic functions for K=2-(n/δ2 > 1 (n being integer or zero and δ =1,2,3 4). The cases for which 0 < K < 1 do not possess negative energy density gradient and therefore are incapable of representing any physically plausible star model. In totality the article provides all the physically plausible exact solutions for the Buchdahl static perfect fluid spheres.

Singularity-free static fluid spheres in general relativity

The relations between the metric coefficients, the energy density, the pressure, and the speed of sound at the center of a perfect fluid sphere which are necessary for singularity-free static solutions are considered. In order to find exact singularity-free static solutions and to construct reasonable star models it is suggested that we modify the known methods of obtaining exact spherically symmetric solutions using these relations. A known class and the new class of such solutions are obtained and the extreme static star model is constructed. At the center of the sphere the equation of state is ultrarelativistic and the sound speed is equal to the speed of light in a vacuum.

Shock waves near the Schwarzschild radius and stability limits for stars

We analyze the time dilation associated with the propagation of a shock wave that moves outward into a static fluid sphere in general relativity. In this way we investigate the possibility that a shock wave inside a star could supply the pressure required to hold up a highly collapsed static outer layer. In such a model, one would observe a highly redshifted, time-independent emissions spectrum during the time interval between the time when the shock wave is formed, and the time when it reaches the star surface. Our conclusion is that the time it takes a shock wave to pass through a surface layer and reach the surface of a star, as seen by an observer in the far field, is on the order of the total mass of the star times a function that tends to infinity as the outer boundary of the star tends to its Schwarzschild radius.

Charged static fluid spheres in general relativity

In this paper, the authors present a new method to extend Pant’ work (see pant D. N.,Astrophys. Space Sci.,215 (1994) 97) to the case of charged fluid spheres. A number of previously known solutions has been rediscovered in the process (see Singh T.et al., Astrophys. Space Sci.,199 (1993) 113, Patino A. and Rago A.,Gen. Rel. Grav.,21 (1989) 637, Whitman P. G. and Burch R. C.,Phys. Rev. D.,24 (1981) 2049, Pant D. N. and Sah A.,Math. Phys.,20 (1979) 2537). Two classes of solutions are obtained and matched at the boundary with the Reissner-Nordstrom metric.

An Exact Model of an Anisotropic Relativistic Sphere

In this paper the field equations of general relativity are solved to obtain an exact solution for a static anisotropic fluid sphere. The solution is free from singularity and satisfies the necessary physical requirements. The physical 3-space of the solution is pseudo-spheroidal. The solution is matched at the boundary with the Schwarzschild exterior solution. Numerical estimates of various physical parameters are briefly discussed.

Static anisotropic fluid spheres inD space-time dimensions

Using the Einstein field equations in the presence of a cosmological constant, the equations which describe the hydrostatic equilibrium of a static anisotropic fluid sphere are obtained inD (D≥4) space-time dimensions. With suitable transformations, the equation of mass-continuity and of hydrostatic equilibrium are given in a non-dimensional form. The formalism thus developed is used to study homogeneous charged fluid spheres in higher dimensions and for these configurations a complete solution is obtained.

Solutions of einstein's field equations for charged static fluid spheres

In this paper the authors have extended Bayin's (1978) work to the case of charged fluid spheres. These solutions are matched at the boundary with the Reissner-Nordstrom solution.

Static anisotropic fluid spheres in general relativity with nonuniform density

An Ansatz developed by Maharaj and Maartens is used to obtain solutions of Einstein's field equations for static anisotropic fluid spheres with nonuniform density. These solutions are matched with the Schwarzschild exterior solution.

The physical properties of an analytic model for a relativistic star

An exact solution of Einstein's equations for a static isentropic perfect fluid sphere is examined in detail. The analysis yields a strong indication that the model isstable with respect to infinitesimal radial pulsations. This means that the temperature is decreasing outwards. We prove that the adiabatic speed of sound is everywhere less than the speed of light if and only if the radius of the sphere is larger than 1.61 times its Schwarzschild radius. We further show that the strong energy condition is fulfilled everywhere if and only if the radius is larger than 1.76 times the Schwarzschild radius. The necessary and sufficient condition for the speed of sound to be decreasing outwards is given, and we find that this criterion is fulfilled if the fluid is causal. Taking the values of the pressure ρ and the density ρ to be somewhere given by the maximum values from Baymet al.'s equation of state, i.e., ρ0=5.1×1014 g cm−3 andp0=7.4×1033 dyne cm−2, we find the maximum mass of the fluid sphere to be 2.5 solar masses.

General relativistic fluid spheres with nonzero vacuum energy density

Bounds are developed for the ratios M/R and m/R for fluid spheres in asymptotically de Sitter or anti-de Sitter space-times, where M is the mass of the fluid sphere, and m is the total mass interior to R: M plus the interior vacuum energy. This represents a generalization of the work of Buchdahl to the case of a nonvanishing vacuum energy density. In the asymptotically de Sitter case, it is possible to construct models which have m/r→ 1/2 . Further, it is shown that static fluid spheres can exist in an asymptotically de Sitter space with vacuum energy density ρv only if their radius satisfies R≤(8πρv)1/2, a maximum radius smaller by a factor of 3−1/2 than the horizon size of the de Sitter space in the absence of a fluid sphere. If the vacuum energy density is negative, then the ratio m/R is shown to be bounded above by the asymptotically flat limit of (4)/(9), and the radius of a positive total mass (m) sphere is shown to be bounded above by R&amp;lt;(2π‖ρv‖)−1/2.

New analytical models for anisotropic spheres in general relativity

Two new exact analytical solutions to Einstein’s field equations representing static fluid spheres with anisotropic pressures are presented. One solution has a maximum value of mass of about 0.42 times the radius of the fluid sphere, dictated by causality and the corresponding values for the surface red shift and the central red shift are 1.58 and 9.03, respectively. The other solution has a maximum mass of about 0.435 times the radius of the fluid sphere and the corresponding red shifts from the surface and from the center are 1.77 and 16.28, respectively. In the low mass limit both solutions reduce to the constant density Schwarzschild interior solution.

A Charged Analogue of the Vaidya?Tikekar Solution

We present here an interior solution of the Einstein-Maxwell equations for a charged static fluid sphere. The physical 3-space t = constant of the solution is spheroidal. The solution is interpreted as an exact relativistic model for a charged superdense star.

Slowly rotating charged fluid spheres in general relativity.

The Einstein-Maxwell field equations for a charged perfect-fluid distribution in a stationary axisymmetric space-time are investigated. Under the assumption of slow rotation, these equations have been reduced to represent slowly rotating charged fluid spheres. It is observed that, similar to the case of slowly rotating uncharged fluid spheres, the field equations split into two parts: viz., the field equations for a static charged fluid sphere and the equations that determine the parameters \ensuremath{\omega} and \ensuremath{\Omega} which represent the angular velocity of the fluid distribution and the angular velocity of the inertial frames along the rotation axis, respectively.

Spherically symmetric perfect fluid solutions in isotropic coordinates

A method of generating solutions of Einstein’s field equations for static fluid spheres is presented. This new method has a very clear advantage since it bypasses the direct resolution of the field equations. One of the solutions obtained is then studied in some detail; it verifies an equation of state of the form p≂αρ+βρ1+1/n.

Electromagnetic mass model of a static charged perfect fluid sphere

Using the results, which they have been already published in two earlier papers (Dionysiou, 1982; Dionysiou and Kostakis, 1983; these papers will hereafter be referred to as Papers I, II, respectively), one can easily see that the total gravitational mass, the density and pressure of a static charged perfect fluid sphere are of electromagnetic origin.