The Rotation and Shear of a String

Whether a string has rotation and shear can be investigated by an anology with a congruence of point particles. Rotation and shear involve first covariant spacetime derivatives of a vector field and, because the metric stress tensor for both the point particle and the string have no such derivatives, the best vector fields can be identified by requiring the conservation of metric stress. It is found that the best vector field is a non-unit accelerating field in x, rather than a unit non-accelerating vector involving the momenta; it is also found that there is an equation obeyed by the spacetime derivative of the Lagrangian L = P a (F a Θ +Fa) using notation which will be defined in the paper. The relationship betwen membranes and fluids is looked at, and it is shown how to produce a membrane with arbitrary Γ for the Γ-equation of state.