Lorentz violation in the linearized gravity

We study some consequences of the introduction of a Lorentz-violating modification term in the linearized gravity, which leads to modified dispersion relations for gravitational waves in the vacuum. We also discuss possible mechanisms for the induction of such a term in the Lagrangian.Comment: Presented at the Fifth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 28-July 2, 201

Two-dimensional Lorentz-violating Chern-Simons-like action

We demonstrate generation of the two-dimensional Chern-Simons-like Lorentz-breaking action via an appropriate Lorentz-breaking coupling of scalar and spinor fields at zero as well as at the finite temperature and via the noncommutative fields method and study the dispersion relations corresponding to this action.Comment: 10 pages, references added, version accepted to Physics Letters

Multidimensional C0C^0 transversality

In 1994, Sakai introduced the property of $C^0$ transversality for two smooth curves in a two-dimensional manifold. This property was related to various shadowing properties of dynamical systems. In this short note, we generalize this property to arbitrary continuous mappings of topological spaces into topological manifolds. We prove a sufficient condition for the $C^0$ transversality of two submanifolds of a topological manifold and a necessary condition of $C^0$ transversality for mappings of metric spaces into $\mathbb{R}^n$.Comment: 9 page