In the framework of Israel formalism the Oppenheimer—Snyder gravitational collapse and a Schwarzschild cavity are studied. The motion of the Oppenheimer—Snyder thick shell can be represented by an appropriate thin shell if the expansion of the shell is great, which is valid in the flat universe.
Starting from Israel equations for spherically symmetric thin shell, the neutral thin shell immersed into different types of Reissner-Nordstrom de-Sitter space-time is constructed. The static and stable configuration of the neutral shell, using only the gravitational field of the charged source as a stabilizing mechanism, is deduced. In particular, two types of shells are studied: a string gas shell and a dust shell with cosmological constant. The dynamical possibilities are also analyzed, including the possibility of child universe creation.
This paper discusses the evolution of a thin spherically symmetric self gravitating phantom shell around the charged shell. The general equations describing the motion of shell with a general form of equation of state are derived. The different types of space-time R± and T± regions and shell motion are classified depending on the parameters of the problem. The mechanical stability analysis of this spherically symmetric thin shell with charge in Reissner- Nordstrom (RN) to linearized spherically symmetric perturbation about static equilibrium solution is carried out.
The starting point in this work is that an expanding shell is accelerated outward by radiation from the remnant star and slowed by ram pressure and accretion as it blows into the interstellar medium. The general relativistic equations of motion for such a shell is formulated. It is reduced to the standard Ostriker Gunn equations, in the non-relativistic limit. Israel formalism is used to describe the development of shell of dust which interacts only gravitationally.
The main aim of this article is to introduce the approximate solution for MHD flow of an electrically conducting Newtonian fluid over an impermeable stretching sheet with a power law surface velocity and variable thickness in the presence of thermal-radiation and internal heat generation/absorption. The flow is caused by the non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The obtaining PDEs are transformed into non-linear system of ODEs using suitable boundary conditions for various physical parameters. We use the Chebyshev spectral method to solve numerically the resulting system of ODEs. We present the effects of more parameters in the proposed model, such as the magnetic parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter and the Prandtl number on the flow and temperature profiles are presented, moreover, the local skin-friction and Nusselt numbers. A comparison of obtained numerical results is made with previously published results in some special cases, and excellent agreement is noted. The obtained numerical results confirm that the introduced technique is powerful mathematical tool and it can be implemented to a wide class of non-linear systems appearing in more branches in science and engineering.