Three Einstein rings: explicit solution and numerical simulation

Mathematical Analysis and Numerical Simulation of Bose-einstein Condensation

On multiple Einstein rings

A number of recent surveys for gravitational lenses have found examples of double Einstein rings. Here, we investigate analytically the occurence of multiple Einstein rings. We prove, under very general assumptions, that at most one Einstein ring can arise from a mass distribution in a single plane lensing a single background source. Two or more Einstein rings can therefore only occur in multi-...

Numerical solution of one-dimensional Burgers equation: explicit and exact-explicit nite di erence methods

This paper presents nite-di erence solution and analytical solution of the nite-di erence approximations based on the standard explicit method to the one-dimensional Burgers equation which arises frequently in the mathematical modelling used to solve problems in uid dynamics. Results obtained by these ways for some modest values of viscosity have been compared with the exact (Fourier) one. It i...

Three-dimensional Einstein-Klein-Gordon system in characteristic numerical relativity

W. Barreto, A. Da Silva, R. Gómez, L. Lehner, L. Rosales, and J. Winicour Centro de Fı́sica Fundamental, Facultad de Ciencias, Universidad de los Andes, Mérida, Venezuela Department of Physics and Astronomy, 2002 Nicholson Hall, Louisiana State University, Baton Rouge, Louisiana 70803-4001, USA Pittsburgh Supercomputing Center, 4400 Fifth Avenue, Pittsburgh, Pennsylvania 15213, USA Department of...

Rotating magnetic solution in three dimensional Einstein gravity

We obtain the magnetic counterpart of the BTZ solution, i.e., the rotating spacetime of a point source generating a magnetic field in three dimensional Einstein gravity with a negative cosmological constant. The static (non-rotating) magnetic solution was found by Clément, by Hirschmann and Welch and by Cataldo and Salgado. This paper is an extension of their work in order to include (i) angula...