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

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We perform a short comparison between the local and linear constitutive tensor $$\chi ^{\lambda \nu \sigma \kappa }$$χλνσκ in four-dimensional electrodynamics, the elasticity tensor $$c^{ijkl}$$cijkl in three-dimensional elasticity theory, and… Click to show full abstract

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

Keywords: dewitt metric; general relativity; electrodynamics elasticity; electrodynamics

Journal Title: General Relativity and Gravitation
Year Published: 2017

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