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In Maxwell electromagnetism, the so-called premetric approach succeeds in separating the purely topological field equation from the constitutive relation between the basic variables. The field equations emerge as consequences of the electric charge and magnetic flux conservation laws. The special metricdependent constitutive tensor recovers the standard Maxwell’s electrodynamics in vacuum. The most general non-metric 4-th order constitutive tensor represents a full range of electromagnetic effects in media and even predicts some new phenomena as skewon, axion and dilaton. Although, in general relativity, the metric tensor of spacetime is essential to represent the gravitational potential, we are able to formulate a gravitational theory with premetric (topological) field equations and a general constitutive law. The field equations emerge as a consequence of the energy-momentum tensor. The 6-th order constitutive tensor describes the relation between the basic field variables. We discuss the irreducible parts of this tensor and their possible physical meaning. With a special constitutive tensor constructed from the metric tensor only, we are able to recover the teleparallel equivalent of GR. With a general constitutive tensor of a metric and non-metric type, we construct a large family of Lorentz violation models of gravity. References [1] F. W. Hehl, Y. Itin and Y. N. Obukhov, “On Kottler’s path: origin and evolution of the premetric program in gravity and in electrodynamics,” Int. J. Mod. Phys. D 25, no. 11, 1640016 (2016) [2] Y. Itin, F. W. Hehl and Y. N. Obukhov, “Premetric equivalent of general relativity: Teleparallelism,” Phys. Rev. D 95, no. 8, 084020 (2017) [3] Yakov Itin, “Premetric representation of mechanics, electromagnetism and gravity”, Int. J. Geom. Methods Mod. Phys. - 15, 1840002 (2018)

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