Focusing of branes in warped backgrounds
Abstract
Description
Branes are embedded surfaces in a given background (bulk) spacetime. Assuming a warped bulk, we investigate, in analogy with the case for geodesics, the notion of {\em focusing} of families of such embedded, extremal 3--branes in a five dimensional background . The essential tool behind our analysis, is the well-known generalised Raychaudhuri equations for surface congruences. In particular, we find explicit solutions of these equations, which seem to show that families of 3--branes can focus along lower dimensional submanifolds depending on where the initial expansions are specified. We conclude with comments on the results obtained and possibilities about future work along similar lines.
11 pages, one figure
11 pages, one figure