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Consistent Lorentz Violation in Flat and Curved Space

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Motivated by the severity of the bounds on Lorentz violation in the presence of ordinary gravity, we study frameworks in which Lorentz violation does not affect the spacetime geometry. We show that there are at least two inequivalent classes of spontaneous Lorentz breaking that even in the presence of gravity result in Minkowski space. The first one generically corresponds to the condensation of tensor fields with tachyonic mass, which in turn is related to ghost-condensation. In the second class, realized in the DGP model or in theories of massive gravity, spontaneous Lorentz breaking is induced by the expectation value of sources. The generalization to de-Sitter space is also discussed.