Comparison of the DeWitt metric in general relativity with the fourth-rank constitutive tensors in electrodynamics and in elasticity theory

TL;DR

This paper compares the DeWitt metric in general relativity with constitutive tensors in electrodynamics and elasticity, highlighting its unique property of having only six independent components.

Contribution

It provides a comparative analysis of the DeWitt metric with other constitutive tensors, revealing its limited degrees of freedom.

Findings

DeWitt metric has only six independent components

Comparison highlights structural similarities and differences

Insights into the tensor's role in different physical theories

Abstract

We perform a short comparison between the local and linear constitutive tensor $\chi^{\lambda\nu\sigma\kappa}$ in four-dimensional electrodynamics (Sec.2), the elasticity tensor $c^{ijkl}$ in three-dimensional elasticity theory (Sec.3), and the DeWitt metric $G^{abcd}$ in general relativity, with ${a,b,\dots=1,2,3}$ (Sec.4). We find that the DeWitt metric has only six independent components.