Jacobi fields in geodesic surface congruences

Abstract

Using the Nambu-Goto string action in the space of the surfaces spanned by closed strings in a spacetime manifold, we investigated the geodesic surface equation in the space of surfaces joining two given strings and the geodesic surface deviation equation in geodesic surface congruence which yields a Jacobi field along a given geodesic surface, and singularities in geodesic surface congruences. In this paper, assuming that the singularity exists in geodesic surface congruences in a conformally symmetric manifold, we compute the Jacobi fields of the geodesic surface deviation equations and observe them. © 2010 World Scientific Publishing Company.