Closed System of Equations on a Brane

Abstract

We obtain a generic closed system of equations on a brane that describes its inner evolution and give a method for extending solutions on the brane to the bulk. We also discuss the cosmological implications of the closed system of equations obtained. We consider bulk spaces with both spacelike and timelike extra dimension, with and without the $Z_2$ symmetry of reflection relative to the brane.

Comments: 11 pages, revtex. Substantially revised version to be published in PLB