Related papers: Rigidly rotating dust solutions depending upon har…
We solve a class of boundary value problems for the stationary axisymmetric Einstein equations corresponding to a disk of dust rotating uniformly around a central black hole. The solutions are given explicitly in terms of theta functions on…
This is the third and last part of a series of 3 papers. Using the same method and the same coordinates as in parts 1 and 2, rotating dust solutions of Einstein's equations are investigated that possess 3-dimensional symmetry groups, under…
We study the radial symmetry properties of stationary and uniformly rotating solutions of the 2D Euler equation in the unit disc, both in the smooth setting and the patch setting. In the patch setting, we prove that every uniformly rotating…
In this work we study the properties of rigidly rotating neutral dust solutions in general relativity. This class of solutions gained relevance recently due to applications to the dynamics of spiral galaxies. We show that this class could…
The equations of secular evolution for dust grains in mean motion resonances with a planet are solved for stationary points. This is done including both Poynting-Robertson effect and stellar wind. The solutions are stationary in semimajor…
We derive evolution and constraint equations for second order perturbations of flat dust homogeneous and isotropic solutions to the Einstein field equations using all scalar, vector and tensor perturbation modes. We show that the…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…
Dust configurations are the simplest models for astrophysical objects. Here we examine the gravitational collapse of an infinite cylinder of dust and give an analytic interior solution. Surprisingly, starting with a cylindrically symmetric…
This is the second 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 class of solutions to the…
Using the Euclidon method, a stationary solution of Einstein's vacuum equations was obtained, describing N rotating axially symmetric masses, which in the absence of rotation describes N arbitrary axially symmetric static masses, for…
We study the observational properties of a class of exact solutions of Einstein's field equations describing stationary, axially symmetric, rigidly rotating dust (i.e. non interacting particles). We ask the question whether such solutions…
We introduce a class of rotating magnetically charged string solutions of the Einstein gravity with a nonlinear electrodynamics source in four dimensions. The present solutions has no curvature singularity and no horizons but has a conic…
In this paper, we present an exact spherically symmetric solution of third order Lovelock gravity in $n$ dimensions which describes the gravitational collapse of a null dust fluid. This solution is asymptotically (anti-)de Sitter or flat…
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…
A new family of exact solutions of the Einstein field equations for static and axially simmetric spacetimes is presented. All the metric functions of the solutions are explicitly computed and the obtained expressions are simply written in…
Using the inverse scattering method to solve the five-dimensional vacuum Einstein equations, we construct an asymptotically flat four-soliton solution as a stationary and bi-axisymmetric solution. We impose certain boundary conditions on…
The Einstein equations are integrated in the presence of two (incoming and outgoing) streams of null dust, under the assumptions of spherical symmetry and staticity. The solution is also written in double null and radiation coordinates and…
The present article is the last in a series of five devoted to the study of the effect of anisotropic pressure on the gravitationnal impact of a stationary rigidly rotating cylindrically symmetric fluid with the use of new exact solutions…
Einstein's equations for a Robertson-Walker fluid source endowed with rotation Einstein's equations for a Robertson-Walker fluid source endowed with rotation are presented upto and including quadratic terms in angular velocity parameter. A…
In this work we have constructed axially symmetric vacuum solutions of the gravitational field equations in a Randall-Sundrum brane. A non-null effective cosmological constant is considered, and asymptotically de Sitter and anti-de Sitter…