The general solution for relativistic spherical shells

We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two values $r_{1}$ and $r_{2}$. The solution is given in three regions, one being the well-known analytical Schwarzschild solution in the outer vacuum region, one being determined analytically in the inner vacuum region, and one being determined ...

We find a new class of exact solutions to the Einstein-Maxwell equations which can be used to model the interior of charged relativistic objects. These solutions can be written in terms of special functions in general; for particular parameter values it is possible to find solutions in terms of elementary functions. Our results contain models found previously for uncharged neutron stars and charged isotropic spheres.

We describe the possible scenarios for the evolution of a thin spherically symmetric self-gravitating phantom shell around the Schwarzschild black hole. The general equations describing the motion of the shell with a general form of equation of state are derived and analyzed. The different types of space-time R- and T-regions and shell motion are classified depending on the parameters of the problem. It is shown that in the case of a positive shell mass there exist three scen...

A family of spherical shells with varying thickness is derived by using a simple Newtonian potential-density pair. Then, a particular isotropic form of a metric in spherical coordinates is used to construct a General Relativistic version of the Newtonian family of shells. The matter of these relativistic shells presents equal azimuthal and polar pressures, while the radial pressure is a constant times the tangential pressure. We also make a first study of stability of both th...

In the process of protostar formation, astrophysical gas clouds undergo thermodynamically irreversible processes and emit heat and radiation to their surroundings. Due the emission of this energy one can envision an idealized situation in which the gas entropy remains nearly constant. In this setting, we derive in this paper interior solutions to the Einstein equations of General Relativity for spheres which consist of isentropic gas. To accomplish this objective we derive a ...

We present a matrix method for obtaining new classes of exact solutions for Einstein's equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein's equations to two independent Riccati type differential equations for which three classes of solutions are obtained. One class of the solutions corresponding to the linear barotropic type fluid with an equation of state $p=\gamma \rho $ is discussed in detail.

We study the behaviour of a specific system of relativistic elasticity in its own gravitational field: a static, spherically symmetric shell whose wall is of arbitrary thickness consisting of hyperelastic material. We give the system of field equations and boundary conditions within the framework of the Einsteinian theory of gravity. Furthermore, we analize the situation in the Newtonian theory of gravity and obtain an existence result valid for small gravitational constants ...

It is shown that almost all known solutions of the kind mentioned in the title are easily derived in a unified manner when a simple ansatz is imposed on the metric. The Whittaker solution is an exception, replaced by a new solution with the same equation of state.

We present a new parametric class of spherically symmetric analytic solutions of the general relativistic field equations in canonical coordinates, which corresponds to causal models of perfect fluid balls. These solutions describe perfect fluid balls with infinite central pressure and infinite central density though their ratio is positively finite and less then one. From the solutions of this class we have constructed two causal models in which outmarch of pressure, density...

In this paper is discussed a class of static spherically symmetric solutions of the general relativistic elasticity equations. The main point of discussion is the comparison of two matter models given in terms of their stored energy functionals, i.e., the rule which gives the amount of energy stored in the system when it is deformed. Both functionals mimic (and for small deformations approximate) the classical Kirchhoff-St.Venant materials but differ in the strain variable us...