Null Strings in Schwarzschild Spacetime

Abstract

The null string equations of motion and constraints in the 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/tensile strings as compared to massless/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.