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The graviton propagation in an asymmetric background is studied. Thebackground is a configuration in the six-dimensional Salam-Sezgin model, inwhich a 3-form H-field turned on [JHEP 0910(2009)086]. The compact dimensionsform a cylindrical space with branes as boundaries. The background getsasymmetry due to the H-field and violates the Lorentz symmetry. We derive thegraviton equation in this background and show that it gets massless modetraveling with superluminal speed. A tower of K-K modes exists with a mass gap.On the other hand, it is known that breaking the Lorentz symmetry on anasymmetric background is constrained by the null energy condition. This no-gotheorem doesn't work well in six-dimensional space-times and by this model weprovide a counterexample for which the null energy condition is satisfied whilethe Lorentz symmetry is gravitationally violated.

Graviton Propagation in an Asymmetric Warped Background: Lorentz Violation and the Null Energy Condition