Related papers: Generating anisotropic fluids from vacuum Ernst eq…
We analyze the stress-energy tensor necessary to generate a general stationary and axisymmetric spacetime. The constraints on the geometry arising from considering a perfect fluid as a source are derived. For a fluid with a nonzero stress…
We establish a new algorithm that generates a new solution to the Einstein field equations, with an anisotropic matter distribution, from a seed isotropic solution. The new solution is expressed in terms of integrals of an isotropic…
Via a straightforward integration of the Einstein equations with cosmological constant, all static circularly symmetric perfect fluid 2+1 solutions are derived. The structural functions of the metric depend on the energy density, which…
We propose a criterion for finding the minimum distance at which an interior solution of Einstein's equations can be matched with an exterior asymptotically flat solution. It is based upon the analysis of the eigenvalues of the Riemann…
We present a simple method to obtain vacuum solutions of Einstein's equations in parabolic coordinates starting from ones with cylindrical symmetries. Furthermore, a generalization of the method to a more general situation is given together…
We present a spherically symmetric solution of the general relativistic field equations in isotropic coordinates for anisotropic neutral fluid, compatible with a super dense star modeling by considering a specific choice of anisotropy…
The problem of two stiff fluids (energy density = pressure) moving radially in spherical symmetry is treated. The metric ansatz is chosen spherically symmetric, conformally static with a multiplicative separation of variables. The first…
In this article we examine a class of wormhole and flux tube like solutions to 5D vacuum Einstein equations. These solutions possess generic local anisotropy, and their local isotropic limit is shown to be conformally equivalent to the…
By a choice of new variables the pressure isotropy condition for spherically symmetric static perfect fluid spacetimes can be made a quadratic algebraic equation in one of the two functions appearing in it. Using the other variable as a…
A class of spherically symmetric spacetimes invariantly defined by a zero flux condition is examined first from a purely geometrical point of view and then physically by way of Einstein's equations for a general fluid decomposition of the…
The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical…
We apply the 1+1+2 covariant semi-tetrad approach to describe a general static and spherically symmetric relativistic stellar object which contains two fluids with anisotropic pressure. The corresponding Tolman-Oppenheimer-Volkoff equations…
We apply a technique, due to Stephani, for generating solutions of the Einstein-perfect fluid equations. This technique is similar to the vacuum solution generating techniques of Ehlers, Harrison, Geroch and others. We start with a ``seed''…
Stationary, axisymmetric, vacuum, solutions of Einstein's equations are obtained as critical points of the total mass among all axisymmetric and $(t,\phi)$ symmetric initial data with fixed angular momentum. In this variational principle…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
We construct asymptotically Euclidean solutions of the vacuum Einstein constraint equations with an apparent horizon boundary condition. Specifically, we give sufficient conditions for the constant mean curvature conformal method to…
The structure of the Einstein field equations describing the gravitational collapse of spherically symmetric isotropic fluids is analyzed here for general equations of state. A suitable system of coordinates is constructed which allows us,…
We introduce a physical characterization of the static and stationary perfect fluid solutions of the Einstein field equations with a single or 2-component perfect fluid sources, according to their gravitoelectric and gravitomagnetic fields.…
We derive a shortcut stationary metric formula for generating imperfect fluid rotating solutions, in Boyer-Lindquist coordinates, from spherically symmetric static ones. We explore the properties of the curvature scalar and stress-energy…
Global stability of the spherically symmetric nonisentropic compressible Euler equations with positive density around global-in-time background affine solutions is shown in the presence of free vacuum boundaries. Vacuum is achieved despite…