All order covariant tubular expansion
Preprint
Abstract
We consider tubular neighborhood of an arbitrary submanifold embedded in a (pseudo-)Riemannian manifold. This can be described by Fermi normal coordinates (FNC) satisfying certain conditions as described by Florides and Synge in \cite{FS}. By generalizing the work of Muller {\it et al} in \cite{muller} on Riemann normal coordinate expansion, we derive all order FNC expansion of vielbein in this neighborhood with closed form expressions for the curvature expansion coefficients. Our result is shown to be consistent with certain integral theorem for the metric proved in \cite{FS}.Keywords
All Related Versions
This publication has 43 references indexed in Scilit:
- On a Coordinate-Independent Description of String Worldsheet TheoryAnnales Henri Poincare, 2013
- Relativistic two-body Coulomb–Breit Hamiltonian in an external weak gravitational fieldPhysics Letters B, 2011
- Fermi coordinates in Schwarzschild spacetime: closed form expressionsGeneral Relativity and Gravitation, 2011
- Fermi Coordinates, Simultaneity, and Expanding Space in Robertson–Walker CosmologiesAnnales Henri Poincare, 2011
- Hydrogen atom and its energy level shifts in de Sitter universeGeneral Relativity and Gravitation, 2009
- A statistical mechanical problem in Schwarzschild spacetimeGeneral Relativity and Gravitation, 2007
- Renormalization of generalized two-dimensional nonlinear σ modelsNuclear Physics B, 1986
- Dimensional regularisation in the presence of large background fieldsAnnals of Physics, 1982
- The background field method and the ultraviolet structure of the supersymmetric nonlinear σ-modelAnnals of Physics, 1981
- Wilson loop in vacuum fieldsNuclear Physics B, 1980