Brane World Models And Darboux Transformations
Abstract
Description
We consider a 5-D gravity plus a bulk scalar field, and with a 3-brane. The Darboux transformation is used to construct some exact solutions. To do this we reduce the system of equations, which describes the 5-D gravity and bulk scalar field to the Schrödinger equation. The jump conditions at the branes lead to the jump potential in the Schrödinger equation. Using the Darboux transformation with these jump conditions, we offer a new exact solution of the brane equations, which represents a generalization of the Rundall-Sundrum solution. For simplicity, the main attention is focused on the case when Hubble root on the visible brane is zero. However, the argument is given that our method is valid in more realistic models with cosmological expansion.
10 pages
10 pages