2002/04/30 by Mark D. Roberts · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cauchy stress tensor #Classical mechanics #Computational Physics and Python Applications #Congruence (geometry) #Covariant derivative #Covariant transformation #Electromagnetic tensor #Exact solutions in general relativity #Geometry #Killing vector field #Mathematical physics #Mathematics #Maxwell's equations #Mechanics #Physics #Quantum mechanics #Relativity and Gravitational Theory #Spacetime #String (physics) #String field theory #Tensor field #Vector field #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/20/3/308
published in Classical and Quantum Gravity 20(3), 507-519 (IOP Publishing) · version 3: some sub/superscript corrections on the internal labels of the Nambu-Goto string, version 2: 17 pages, result generalized and contact established with the approach of others
arxiv created 2002/08/25 · openalex publication_date 2003/01/15 · arxiv updated 2011/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Whether a string has rotation and shear can be investigated by an analogy 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 using a notation which will be defined in the paper. The relationship between membranes and fluids is looked at, and it is shown how to produce a membrane with arbitrary Γ for the Γ-equation of state.