1993/04/30 by Jemal Guven
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Covariant transformation #Curvature #Geometry #Mathematical physics #Mathematics #Physics #Quantum mechanics #Scalar (mathematics) #Spacetime #Topological defect #Topology (electrical circuits) #Torsion (gastropod) #gr-qc
paper · pdf · doi:10.1103/physrevd.48.5562
published as Phys.Rev. D48 (1993) 5562-5569
arxiv created 1993/08/25 · openalex publication_date 1993/12/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The evolution of small irregularities in a topological defect which propagates on a curved background spacetime is examined. These are described by a system of coupled scalar wave equations on the world sheet of the unperturbed defect which is not only manifestly covariant under world-sheet diffeomorphisms but also under local normal frame rotations. The scalars couple both through the surface torsion of the background world sheet geometry which acts as a vector potential and through an effective mass matrix which is a sum of a quadratic in the extrinsic curvature and a linear term in the spacetime curvature. The coupling simplifies enormously for many physically interesting geometries. This introduces a framework for examining the stability of topological defects generalizing both our earlier work on the perturbations of domain walls and the work of Garriga and Vilenkin on perturbations about a class of spherically symmetric defects in de Sitter space.