Null strings in Schwarzschild spacetime

The null string equations of motion and constraints in Schwarzschild spacetime are,given. The solutions are those of the null geodesics of general relativity appended by a null string constraint in which the ''constants of motion'' depend on the world-sheet spatial coordinate. Because of the extended nature of a string, the physical interpretation of the solutions is completely different from the point particle case. In particular, a null string is generally not propagating in a plane through the origin, although each of its individual points is. Some special solutions are obtained and their physical interpretation is given. Especially, the solution for a null string with a constant radial coordinate r moving vertically from the south pole to the north pole around the photon sphere is presented. A general discussion of classical null or tensile strings as compared to massless or massive particles is given. For instance, tensile circular solutions with a constant radial coordinate r do not exist at all. The results are discussed in relation to the previous literature on the subject.