All order covariant tubular expansion
arXiv:1203.1151 · doi:10.1142/S0129055X13500190
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}.
27 pages. Corrected an error in a class of coefficients resulting from a typo. Integral theorem and all other results remain unchanged
References in corpus (10)
- Fermi coordinates, simultaneity, and expanding space in Robertson-Walker cosmologies
- General Transformation Formulas for Fermi-Walker Coordinates
- Constrained Quantum Systems as an Adiabatic Problem
- Applications of Two-Body Dirac Equations to the Meson Spectrum with Three versus Two Covariant Interactions, SU(3) Mixing, and Comparison to a Quasipotential Approach
- Exact Fermi coordinates for a class of spacetimes
- The Energy-Level Shifts of a Stationary Hydrogen Atom in Static External Gravitational Field with Schwarzschild Geometry
- A Statistical Mechanical Problem in Schwarzschild Spacetime
- Fermi coordinates in Schwarzschild spacetime: closed form expressions
- DeWitt-Virasoro construction
- Relativistic Two-Body Coulomb-Breit Hamiltonian in an External Weak Gravitational Field