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We develop a relativistic variational model for a nematic liquid crystalinteracting with an electro- magnetic field. The constitutive relation for ageneral anisotropic uniaxial diamagnetic and dielectric medium is analyzed. Wediscuss light wave propagation in this moving uniaxial medium, for which thecorresponding optical metrics are identified explicitly. A Lagrangian for thecoupled system of a nematic liquid crystal and the electromagnetic field isconstructed, from which a complete set of equations of motion for the system isderived. The canonical energy-momentum and spin tensors are systematicallyobtained. We compare our results with those within the non-relativistic models.As an application of our general formalism, we discuss the so-calledAbraham-Minkowski controversy on the momentum of light in a medium.

Relativistic Lagrangian model of a nematic liquid crystal interacting with an electromagnetic field