Generalized Tensor Analysis Method Applied to Non-time-orthogonal Coordinate Frames

TL;DR

This paper introduces a generalized tensor analysis method for non-time-orthogonal frames, enabling accurate analysis of phenomena like electrodynamics around rotating bodies, and successfully predicts experimental results.

Contribution

It presents a novel covariant tensor analysis approach for non-orthogonal frames, including specific procedures for component conversion and application to electrodynamics.

Findings

Method accurately predicts Wilson/Wilson experiment results

Method applicable to rotating spacetime scenarios

Provides a systematic tensor analysis framework for non-orthogonal frames

Abstract

A generalized covariant method of analysis applicable to frames for which time is not orthogonal to space, such as spacetime around a star possessing angular momentum or on a rotating disk, is presented. Important aspects of such an analysis are shown to include i) use of the physically relevant contravariant or covariant component form for a given vector/tensor, ii) conversion of physical (measured) components to generalized coordinate components prior to tensor analysis, iii) use of generalized covariant constitutive equations during tensor analysis, and iv) conversion of coordinate components back to physical components after tensor analysis. The method is then applied to electrodynamics in a rotating frame, and shown to predict the results of the Wilson/Wilson and Roentgen/Eichenwald experiments.