Líquidos nemáticos e relatividade geral

André dos Reis Bombardi

In the mean 80´s, it was proposed that the rheologic properties of liquidcrystal could be obtained through affine transformation, in which the interaction potential of aspheric molecule is deformed to assume the ellipsoidal shape of potential liquid crystal´smolecular interaction. When this procedure is done point to point, the usuals derivatives donot get transformed into usual covariant vectors, and consequently, they should be substitutedby covariant derivatives. Mathematically, the connection approach to Nematic liquid crystalresembles the gravitational field described by Relativity Theory, which provides sufficientdata to study the correspondences between these two theories. The first result presented is thedemonstration that the approach of the affine connection reveals that the mathematicaldescription of Nematic textures has necessarily an intrinsic curved surface. Consequently,some textures of Nematic liquid crystals may be described through a similar equation toEinstein´s General Relativity, with the elastic stress tensor taking place of the energymomentumtensor. The null curvature limit of this equation is the generalization of Poisson´sequation, which describes the generated textures by liquid crystal´s defects, with theadvantage, in this case, of being temperature dependent.

Líquidos nemáticos e relatividade geral

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