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We perform a short comparison between the local and linear constitutivetensor $\chi^{\lambda\nu\sigma\kappa}$ in four-dimensional electrodynamics(Sec.2), the elasticity tensor $c^{ijkl}$ in three-dimensional elasticitytheory (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 sixindependent components.

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