Stable knotted strings

Abstract

We solve the Cauchy problem for the relativistic closed string in Minkowski space M 3+1, including the cases where the initial data has a knot like topology. We give the general conditions for the world sheet of a closed knotted string to be a time periodic surface. In the particular case of zero initial string velocity the period of the world sheet is proportional to half the length ( l) of the initial string and a knotted string always collapses to a link for t = l/4. Relativistic closed strings are dynamically evolving or pulsating structures in spacetime, and knotted or unknotted like structures remain stable over time. The generation of arbitray n-fold knots, starting with an initial simple link configuration with non zero velocity is possible.