Related papers: Rigidly rotating dust in general relativity
These notes address the planar gravitational wave solutions of general relativity in empty space-time, and analyze the motion of test particles in the gravitational wave field. Next we consider related solutions of the Einstein equations…
The gravitational field of an isolated, axisymmetric flat disk of spinning dust is calculated approximately in the weak-field limit of quasi-metric gravity. Boundary conditions single out the exponential disk as a "preferred" physical…
We study dynamical gravitational collapse in a theory with an infinite tower of higher-derivative corrections to the Einstein-Hilbert action and we show that, under very general conditions, it leads to the formation of regular black holes.…
We investigate gravitational properties of thin planar wall solutions of the Einstein's equations in the weak field approximation. We find the general metric solutions and discuss the behavior of a particle placed initially at rest to one…
We discuss the exact solution of Einstein's equation corresponding to a static and plane symmetric distribution of matter with constant positive density located below $z=0$ matched to vacuum solutions.
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…
We investigate spherically symmetric gravitational collapse of thick matter shell without radiation in the Einstein gravity with cosmological constant. The orbit of the infalling thick matter is determined by imposing an equation of state…
After a brief summary of the foundations of general relativity, we will concentrate on the stationary exact solutions of the Einstein and Einstein-Maxwell equations. A number of these solutions can be interpreted as black holes,…
We suggest a limit of Einstein equations incorporating the state $g_{\mu\nu}=0$ as a solution. The large scale behavior of this theory has interesting properties. For a spherical source, the velocity profile for circular motions is of the…
We study the exact solution of Einstein's field equations consisting of a ($n+2$)-dimensional static and hyperplane symmetric thick slice of matter, with constant and positive energy density $\rho$ and thickness $d$, surrounded by two…
A solution to Einstein's field equations via the Friedman equations is shown to produce a cosmological model that is in exact agreement with the measurements made by the dark energy astronomers. All the essential physical parameters are…
We consider stationary rotating cylindrically symmetric dust spacetimes. We first show that the Maitra spacetime is the unique non-rigidly (non null shear scalar) rotating solution with a regular axis and that is the most general one of the…
We study the stationary Boltzmann equation in a thin slab for a rarefied gas for which the molecular mean free path is comparable to the film thickness. We prove that there exists a solution which converges, in the hydrodynamic limit, to a…
A scalar field generalization of Xanthopoulos's cylindrically symmetric solutions of the vacuum Einstein equation is obtained. The obtained solution preserves the properties of the Xanthopoulos solution, which are regular on the axis,…
The theoretical description of compact structures that share some key features with mass varying particles allows for a simple analysis of equilibrium and stability for massive stellar bodies. We investigate static, spherically symmetric…
We show that the Schwarzschild solution can be embedded in a class of nonstandard solutions of the vacuum Einstein's equations with arbitrary rotation curves. These nonstandard solutions have to be taken as physical if dark matter as needed…
We find analytical solutions describing the collapse of an infinitely long cylindrical shell of counter-rotating dust. We show that--for the classes of solutions discussed herein--from regular initial data a curvature singularity inevitably…
The paper is concerned with the Einstein equations for a spherically symmetric static distribution of anisotropic matter. The equations are cast into a system of Fuchsian type ODE for certain scalar invariants of the strain. And then the…
We analyze the spherically symmetric Einstein field equation with a massless complex scalar field. We can use the Newtonian solutions to fit the rotation curve data of spiral and dwarf galaxies. From the general relativistic solutions, we…
We investigate some cylindrically symmetric nonstationary and nonstatic solutions of Einstein field equations. We first study some physical properties of a solution which can be considered as Kasner generalization of static Levi-Civita…