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

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 $a,b,\cdots =1,2,3$ (Sec.4). We find that the DeWitt metric has only six independent components.