Hořava–Lifshitz gravity has covariance only under the foliation-preserving diffeomorphism. This implies that the quantities on the constant-time hypersurfaces should be regular. In the original theory, the projectability condition, which strongly restricts the lapse function, is proposed. We assume that a star is filled with a perfect fluid with no-radial motion and that it has reflection symme...

We use the Wetterich equation for foliated spacetimes to study the renormalization group flow of projectable Hořava-Lifshitz gravity coupled to n Lifshitz scalars. Using novel results for anisotropic heat kernels, the matter-induced beta functions for the gravitational couplings are computed explicitly. The renormalization group flow exhibits an UV attractive anisotropic Gaussian fixed point wh...

We describe all FMm1,m2,n1,n2 -natural operators D : Qproj-proj QT ∗ transforming projectable-projectable classical torsion-free linear connections ∇ on fibred-fibred manifolds Y into classical linear connections D(∇) on cotangent bundles T ∗Y of Y . We show that this problem can be reduced to finding FMm1,m2,n1,n2 -natural operators D : Qproj-proj (T ∗,⊗pT ∗⊗⊗qT ) for p = 2, q = 1 and p = 3, q...

Statecharts is a language for the speciication of reactive systems. Semantics of Statecharts enforcing causality and synchronous hypothesis cannot be modular, and therefore do not allow general bottom-up construction of speciication and reuse of components. In this paper we propose both a global-consistent and a non global-consistent semantics which, in contrast to the known ones, are projectab...

Using the multiplicity of solutions for the projectable case of the covariant extension of Hořava-Lifshitz gravity, we show that an appropriate choice for the auxiliary field allows for an effective description of galaxy rotation curves. This description is based on static and spherically symmetric solutions of covariant Hořava-Lifshitz gravity and does not require Dark Matter.

In the article (Martinez and Zenk, Algebra Universalis, 50, 231–257, 2003.), the authors studied several conditions on an algebraic frame L. In particular, four properties called Reg(1), Reg(2), Reg(3), and Reg(4) were considered. There it was shown that Reg(3) is equivalent to the more familiar condition known as projectability. In this article we show that there is a nice property, which we c...