The general solution for relativistic spherical shells

We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the anisotropy factor. The energy density and both radial and tangential pressures are finite and positive inside the anisotropic star. Numerical results show that the basic physical parameters (mass and radius) of the model can describe realistic astro...

General relativistic spherically symmetric matter field with a vanishing stress energy scalar is analyzed. Procedure for generating exact solutions of the field equations for such matter distributions is given. It is further pointed out that all such type I spherically symmetric fields with distinct eignvalues in the radial two space can be treated as a mixture of isotropic and directed radiations. Various classes of exact solutions are given. Junction conditions for such a m...

Following a solution generating technique introduced recently by one of us, we transform the Einstein static Universe into a two - fold infinity class of physically acceptable exact perfect fluid solutions of Einstein's equations. Whereas the entire class of solutions can be considered as generalizations of the familiar Tolman IV solution, no member of the class can be written explicitly in isotropic coordinates. Further, except for a set of measure zero, no member of the cla...

In this paper we study the isotropic cases of static charged fluid spheres in general relativity. For this purpose we consider two different specialization and under these we solve the Einstein-Maxwell field equations in isotropic coordinates. The analytical solutions thus we obtained are matched to the exterior Reissner-Nordstr\"om solutions which concern with the values for the metric coefficients $e^{\nu}$ and $e^{\mu}$. We derive the pressure, density, pressure-to-density...

Spherically gravitational collapse towards a black hole with non-zero tangential pressure is studied. Exact solutions corresponding to different equations of state are given. We find that when taking the tangential pressure into account, the exact solutions have three qualitatively different endings. For positive tangential pressure, the shell around a black hole may eventually collapse onto the black hole, or expand to infinity, or have a static but unstable solution, depend...

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-Nordstr\"om spacetime. 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 the model parameters. A large class of solutions ob...

We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing the model parameters in our formulation, we generate closed-form solutions which may be treated as anisotropic generalization of a large class of solutions describing isotropic fluid spheres. From the resultant solutions, a particular soluti...

This article presents some aspects and experience in the use of algebraic manipulation software applied to general relativity. Some years ago certain results were reported using computer algebra platforms, but the growing popularity of graphical platforms such as Maple allows us to approach the problem of the simplifications of many expressions from another point of view. Some simple algebraic programming procedures are presented (in Maple with the GrTensorIII package) to obt...

The Vlasov-Einstein system describes the evolution of an ensemble of particles (such as stars in a galaxy, galaxies in a galaxy cluster etc.) interacting only by the gravitational field which they create collectively and which obeys Einstein's field equations. The matter distribution is described by the Vlasov or Liouville equation for a collisionless gas. Recent investigations seem to indicate that such a matter model is particularly suited in a general relativistic setting ...

We study some properties of static spherically symmetric elastic bodies in general relativity using both analytical and numerical tools. The materials considered belong to the class of John elastic materials and reduce to perfect fluids when the rigidity parameter is set to zero. We find numerical support that such elastic bodies exist with different possible shapes (balls, single shells and multiple shells) and that their gravitational redshift can be very large ($z\approx 2...