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.

16 pages, REVTEX, no figures

References in corpus (6)

• Planetoid String Solutions in 3 + 1 Axisymmetric Spacetimes
• Friedmann Universes and Exact Solutions in String Cosmology
• String dynamics in cosmological and black hole backgrounds: The null string expansion
• Schild's Null Strings in Flat and Curved Backgrounds
• Tension as a Perturbative Parameter in Non--Linear String Equations in Curved Space--Time
• On a Possibility of Membrane Cosmology

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• Exact String Solutions in Nontrivial Backgrounds
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• Gravitational Interactions of Finite Thickness Global Topological Defects with Black Holes
• Strings in Homogeneous Background Spacetimes
• Null Strings in Kerr Spacetime
• Null Branes in Curved Backgrounds
• Optical equations for null strings
• Null Cosmic Strings: Scattering by Black Holes, Optics and Spacetime Content
• Electrodynamics under Action of Null Cosmic Strings
• Null Strings and Membranes in Demianski-Newman Background
• Open Cosmic Strings in Black Hole Space-Times
• On light-like extremal surfaces in curved spacetimes