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In this work we focus on a toy model: (3+1)-dimensional Hov{r}ava-Lifshitz gravity coupling with an anisotropic electromagnetic (EM) field which is generated through a Kaluza-Klein reduction of a (4+1)-dimensional Hov{r}ava-Lifshitz gravity. This model exhibits a remarkable feature that it has the same velocity for both gravitational and electromagnetic waves. This feature makes it possible to restrict the parameters of the theory from GRB 170817A. In this work we use this feature to discuss possible constraints on the parameter $beta$ in the theory, by analyzing the possible Lorentz invariance violation effect of the GRB 170817A. This is achieved by analyzing potential time delay of gamma-ray photons in this event. It turns out that it places a stringent constraint on this parameter. In the most ideal case, it gives $|1-sqrt{beta}|<(10^{-19}-10^{-18})$.
We discuss some aspects of the Horava-Lifshitz cosmology with different matter components considered as dominants at different stages of the cosmic evolution (each stage is represented by an equation of state pressure/density=constant). We compare co
Hov{r}ava gravity breaks boost invariance in the gravitational sector by introducing a preferred time foliation. The dynamics of this preferred slicing is governed, in the low-energy limit suitable for most astrophysical applications, by three dimens
In this paper, we have studied non stationary dust spherically symmetric spacetime, in general covariant theory ($U(1)$ extension) of the Hov{r}ava-Lifshitz gravity with the minimally coupling and non-minimum coupling with matter, in the post-newtoni
We investigate the Hamiltonian structure of linearized extended Hov{r}ava- Lifshitz gravity in a flat cosmological background following the Faddeev-Jackiws Hamiltonian reduction formalism. The Hamiltonian structure of extended Hov{r}ava-Lifshitz grav
We investigate string-like solutions in four dimensions based on Hov{r}ava-Lifshitz gravity. For a restricted class of solutions where the Cotton tensor vanishes, we find that the string-like solutions in Einstein gravity including the BTZ black stri