Related papers: The Levi-Civita spacetime
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…
Caustics-envelopes formed by the trajectories of fluid particles-arise in proposed dynamical extensions for shell-crossing singularities occurring in the Einstein-dust system. In this study, a local existence result is established,…
We consider a Lemaitre - Tolman - Bondi type space-time in Einstein gravity with the Gauss-Bonnet combination of quadratic curvature terms, and present exact solution in closed form. It turns out that the presence of the coupling constant…
This is the third in a series of papers on the construction of explicit solutions to the stationary axisymmetric Einstein equations which can be interpreted as counter-rotating disks of dust. We discuss the physical properties of a class of…
The Levi-Civita (LC) solution is matched to a cylindrical shell of an anisotropic fluid. The fluid satisfies the energy conditions when the mass parameter $\sigma$ is in the range $0 \le \sigma \le 1$. The mass per unit length of the shell…
In this paper, we take dust matter and investigate static spherically symmetric solution of the field equations in metric f(R) gravity. The solution is found with constant Ricci scalar curvature and its energy distribution is evaluated by…
We explore the gravitational collapse of a spherically symmetric dust cloud in the Einstein-Gauss-Bonnet gravity without a cosmological constant, and obtain three families of LTB-like solutions. It is shown that the Gauss-Bonnet term has a…
If the causality condition [the speed of sound always remains less than that of light in vacuum, i. e., $v \leq c = 1$] is imposed on the spheres of homogeneous energy density, the `ratio of the specific heats', $\gamma \leq 2.59457$,…
Known examples in plane symmetry or Gowdy symmetry show that given a $1$-parameter family of solutions to the vacuum Einstein equations, it may have a weak limit which does not satisfy the vacuum equations, but instead has a non-trivial…
We present the exact solution of Einstein's equation corresponding to a static and plane symmetric distribution of matter with constant positive density located below $z=0$. This solution depends essentially on two constants: the density…
We propose a revised formulation of General Relativity for cosmological settings, in which the Einstein constant varies with the energy density of the Universe. We demonstrate that this modification has only phenomenological impact of…
We numerically study the dynamics of an imploding hollow cylinder composed of dust. Since there is no cylindrical black hole in 4-dimensional spacetime with physically reasonable energy conditions, a collapsed dust cylinder involves a naked…
In this work, we obtained exact solutions of Einstein's field equations for plane symmetric cosmological models by assuming that thy admit conformal motion. The space-time geometry of these solutions is found to be nonsingular, non-vacuum…
A family of exact solutions is presented which represents a rigidly rotating cylinder of dust in a background with a negative cosmological constant. The interior of the infinite cylinder is described by the Godel solution. An exact solution…
The Einstein equations for an inhomogeneous irrotational dust universe are analysed. A set of mild assumptions, all of which are shared by the standard FLRW type scenarios, results in a model that depends only on the distribution of scalar…
The Tolman-Bondi and Vaidya solutions are two solutions to Einstein equations which describe dust particles and null fluid, respectively. We show that it is possible to match the two solutions in one single spacetime, the…
Einstein's equations are solved for spherically symmetric universes composed of dust with tangential pressure provided by angular momentum, L(R), which differs from shell to shell. The metric is given in terms of the shell label, R, and the…
We consider gravitational collapse in the recently proposed 4D limit of Einstein-Gauss-Bonnet gravity. We show that for collapse of a sphere made of homogeneous dust the process is qualitatively similar to the case of pure Einstein's…
The global properties of static perfect-fluid cylinders and their external Levi-Civita fields are studied both analytically and numerically. The existence and uniqueness of global solutions is demonstrated for a fairly general equation of…
We use ALMA observations of four sub-millimetre galaxies (SMGs) at $z\sim2-3$ to investigate the spatially resolved properties of the inter-stellar medium (ISM) at scales of 1--5 kpc (0.1--0.6$''$). The velocity fields of our sources,…