Related papers: Differentially rotating disks of dust
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 first in a series of papers on the construction of explicit solutions to the stationary axisymmetric Einstein equations which describe counter-rotating disks of dust. These disks can serve as models for certain galaxies and…
In this paper, solutions to the Ernst equation are investigated that depend on two real analytic functions defined on the interval [0,1]. These solutions are introduced by a suitable limiting process of Backlund transformations applied to…
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…
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…
Disks of collisionless particles are important models for certain galaxies and accretion disks in astrophysics. We present here a solution to the stationary axisymmetric Einstein equations which represents an infinitesimally thin dust disk…
For a stationary and axisymmetric spacetime, the vacuum Einstein field equations reduce to a single nonlinear PDE in two dimensions called the Ernst equation. By solving this equation with a {\it Dirichlet} boundary condition imposed along…
We review explicit solutions to the stationary axisymmetric Einstein-Maxwell equations which can be interpreted as disks of charged dust. The disks of finite or infinite extension are infinitesimally thin and constitute a surface layer at…
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…
The two known exact solutions of Einstein's field equations describing rotating objects of physical significance - a black hole and a rigidly rotating disk of dust - are discussed using a single mathematical framework related to Jacobi's…
Stability of circular orbits of the dust particles within a charged rotating disc of dust with respect to perturbations in the equatorial plane is analyzed. Within Einstein-Maxwell theory, the charged rotating disc of dust is an…
We write down the relevant field equations for a stationary axially symmetric rigidly rotating dust source in such a way that the general solution depends upon the solution of an elliptic equation and upon harmonic functions. Starting with…
The exact global solution of the Einstein equations [Neugebauer & Meinel, Phys. Rev. Lett. 75 (1995) 3046] describing a rigidly rotating, self-gravitating disk is discussed. The underlying matter model is a perfect fluid in the limit of…
We present an algorithm for obtaining the post-Newtonian expansion of the asymptotically flat solution to the Einstein-Maxwell equations describing a rigidly rotating disc of dust with a constant specific charge. Explicit analytic…
A solution to the Einstein field equations that represents a rigidly rotating dust accompanied by a thin matter shell of the same type is found.
A new family of exact solutions of the Einstein-Maxwell equations for static axially symmetric spacetimes is presented. The metric functions of the solutions are explicitely computed and are simply written in terms of the oblate spheroidal…
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…
It is shown that the interior solution of axially symmetric, stationary and rigidly rotating dust configurations is completely determined by the mass density along the axis of rotation. The particularly interesting case of a mass density,…
We demonstrate how the solution to an exterior Dirichlet boundary value problem of the axisymmetric, stationary Einstein equations can be found in terms of generalized solutions of the Backlund type. The proof that this generalization…
We use a Harrison transformation on solutions to the stationary axisymmetric Einstein equations to generate solutions of the Einstein-Maxwell equations. The case of hyperelliptic solutions to the Ernst equation is studied in detail.…