Static Perfect Fluid Research Articles

Cylindrical universes with heat and null radiation flow

We have discussed cylindrically symmetric models with the Kasnerian time evolution incorporating heat flow and null radiation flow with the perfect fluid. In the case of heat flow the Kasner spacetime is the matter-free limit of the model. We establish a general result that a static perfect fluid distribution will on Kasnerization (introduce t 4/3 , t 4/3 , and t −2/3 in the coefficients of dr 2 , dΦ 2 , and dz 2 ) yield a time-dependent distribution with the same equation of state and with or without heat flow

Stationary and static axisymmetric perfect fluid solutions

Using a certain formalism for the stationary axisymmetric problem with source a rigidly rotating perfect fluid it is shown that under specific assumptions, covariantly imposed, the field equations are reduced to a system of two ordinary second order differential equations. Two known metrics are special solutions of this system. In addition two static axisymmetric perfect fluid solutions, with a spherically symmetric limit, are derived explicitly.

Static spherically-symmetric perfect fluids with pressure equal to energy density

The present Letter represents an exact, static, and spherically-symmetric solution of Einstein's field equations for a homogeneous perfect fluid core surrounded by a field of Zeldovich's fluid which is asymptotically homaloidal.

On the spherical symmetry of static perfect fluids in general relativity

We present a theorem which establishes uniqueness, in particular spherical symmetry, of a wide class of general relativistic, static perfect-fluid models provided there exists a spherically symmetric model with the same equation of state and surface potential. The method of proof, which is inspired by recent work of Masood-ul-Alam, is illustrated by demonstrating uniqueness of a class of solutions due to Buchdahl which correspond to an extreme case of the inequality on the equation of state required by our theorem.

Perfect fluids with conformal motion

The axisymmetric rigidly rotating or static perfect fluid solutions admitting a proper conformai Killing vector orthogonal to the orbits of the two-dimensional group of motions are determined.

General exact solution for homogeneous time-dependent self-gravitating perfect fluids

A procedure to obtain the general exact solution of Einstein equations for a self-gravitating spherically symmetric static perfect fluid obeying an arbitrary equation of state is applied to time-dependent Kantowski–Sachs line elements (with spherical, planar, and hyperbolic symmetry). As in the static case, the solution is generated by an arbitrary function of the independent variable and its first derivative. To illustrate the results, the whole family of (plane-symmetric) solutions with a ‘‘gamma-law’’ equation of state is explicitly obtained in terms of simple known functions. It is also shown that, while in the static plane-symmetric line element, every metric is in one to one correspondence with a ‘‘partner metric’’ (both originated from the same generatrix function); in this case every generatrix function uniquely determines one metric.

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.

Some static and nonstatic perfect fluid models in general relativity

The Einstein field equations have been solved for cylindrically symmetric spacetimes with perfect fluid source. Out of three models derived, one is static and the other two are nonstatic. Certain physical and geometrical properties of the models have been examined.

General exact solutions of Einstein equations for static perfect fluids with spherical symmetry

The gravitational field equations for a spherical symmetric perfect fluid are completely solved. The general analytical solution obtained depends on an arbitrary function of the radial coordinate. As illustrations of the proposed procedure the exterior and interior Schwarzschild solutions are regained.

The topology of asymptotically Euclidean static perfect fluid space-time

It is shown that a geodesically complete, asymptotically Euclidean, static perfect fluid space-time satisfying the time-like convergence condition and having a connected fluid region is diffeomorphic to ℝ3×ℝ.

On the spherical symmetry of static perfect fluid spacetimes and the positive-mass theorem

Although it is considered physically evident, a rigorous proof that a static stellar model is spherically symmetric is still lacking. The author discusses the relevance of the positive-mass theorem in proving the spherical symmetry of a static stellar model. As an example the author proves the uniqueness of a particular static perfect fluid solution due to Wyman (1930) using the positive-mass theorem.

Static relativistic perfect fluids with spherical, plane, or hyperbolic symmetry

This article examines the Einstein field of equations of general relativity, when the source of the gravitational field is a perfect fluid, and the geometry is static and possesses spherical, plane, or hyperbolic symmetry. This examination unifies, extends, and amends some earlier works. It is shown that a previous qualitative treatment of static spherically symmetric perfect fluids that obey a γ-law equation of state can be extended to include the cases of plane and hyperbolic symmetry. In the case of plane symmetry, the exact solution is provided for general values of γ. This indicates defects in an earlier prescription that was given for a general equation of state.

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.

Static spin-polarized cylinder in the Einstein-Cartan theory of gravitation

An exact solution of the Einstein-Cartan field equations is obtained, which represents the gravitational field of a static perfect fluid cylinder with a net spin polarization along its axis of symmetry. It is found that the gravitational field is stationary, with the cylinder's spin giving rise to inertialframe dragging.

A source for the Reissner-Nordstrøm metric

An exact solution of the coupled Einstein-Maxwell equations representing the gravitational field in the interior of a sphere of charged incoherent matter in equilibrium is obtained which is a charged analogue of the static perfect fluid sphere solution with spheroidal 3-space obtained by Vaidya & Tikekar.

Solutions of Einstein-Maxwell field equations for a static charged perfect fluid shphere

The object of this paper is to give a new mathematical and physical method of finding explicit analytical interior solutions of the Einstein-Maxwell field equations of a static perfect fluid sphere with charge.

Ellipticity of static perfect fluids in preferred-frame theories of gravity

It is shown that in any metric theory with the parametrized-post-Newtonian parameter ${\ensuremath{\alpha}}_{2}\ensuremath{\ne}0$ (for general relativity ${\ensuremath{\alpha}}_{2}=0$) a static---in the rest frame---perfect fluid moving with velocity $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}$ relative to the preferred frame of the Universe, in empty space, cannot have a spherically symmetric configuration and is oblate for ${\ensuremath{\alpha}}_{2}>0$ and prolate for ${\ensuremath{\alpha}}_{2}<0$, with respect to the direction of motion.

The Melnick–Tabensky solutions have high symmetry

Melnick and Tabensky recently gave a class of static perfect fluid solutions of Einstein’s equations in which the metric (in co-moving coordinates) takes the conformastat form. In this paper we point out that all these solutions have spherical or plane or pseudospherical symmetry.

Equilibrium of a static charged perfect fluid sphere

A study is developed for treating Einstein-Maxwell's equations, applied to a static perfect fluid sphere with charge, in a such a manner to generalize the Oppenheimer and Volkoff hydrostatic equilibrium equation.

Static Perfect Fluid in the Einstein-Cartan Theory

It is shown that the static perfect fluid solutions of the Einstein-Cartan equations can be obtained from the known solutions of the Einstein equations by redefining the density of matter and the pressure. In the case of spherically symmetric perfect fluid distribution, the contribution of the spin of the matter and the torsion of the geometry remains arbitrary. Different equations of state can be obtained by choosing the spin differently.