T-violation tests for relativity principles

We consider the implications of a violation of the equivalence principle or of Lorentz invariance in the neutrino sector for the T-asymmetry $\Delta P_T \equiv P(\nu_{\alpha} \to \nu_{\beta}) - P(\nu_{\beta} \to \nu_{\alpha})$ in a three-flavour framework. We find that additional mixing due to these mechanisms, while obeying all present bounds, can lead to a substantial enhancement, suppression, and/or sign change in $\mathrm{\Delta }{P}_T$ for the preferred energies and baselines of a neutrino factory. This in turn allows for the possibility of improving existing constraints by several orders of magnitude.