Year: 2001
Type: article
Abstract: We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific derivatives are described: convective, corotational and directional. The covariance is made explicit by working in arbitrary time-dependent coordinates, instead of restricting to Eulerian or Lagrangian coordinates. The commutator of covariant time and space derivatives is interpreted in terms of a time-curvature that shares many properties of the Riemann curvature tensor, and reflects nontrivial time dependence of the metric.
Author: Jean-Luc Thiffeault
Institution: Columbia University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2081471296