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Considerations on the Graviton Excitation Modes of Horava-Lifshitz Gravity

A new set of projection operators is constructed to suitably handle non-relativistic theories of gravity with anisotropic scaling, including the ones with parity-violating terms. This alternative procedure allows us to discuss unitarity and spectral properties for different formulations of the Horava-Lifshitz gravity. This task, that generally involves lengthy algebraic steps, becomes more systematic and greatly simplified in terms of the projectors we work out. Moreover, this procedure allows us to fix the number of propagating degrees of freedom and the structure of gauge symmetries is readily determined. In order to test the efficacy of the technique at hand, the unitarity and low-energy regime of a general Horava-Lifshitz Gravity model are investigated.