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Register a new userShear-free Dust Solution in General Covariant Hov{r}ava-Lifshitz Gravity
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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-newtonian approximation (PPN) in the infrared limit. The Newtonian prepotential $varphi$ was assumed null. The aim of this work is to know if we can have the same spacetime, as we know in the General Relativity Theory (GRT), in Hov{r}ava-Lifshitz Theory (HLT) in this limit. We have shown that there is not an analogy of the dust solution in HLT with the minimally coupling, as in GRT. Using non-minimum coupling with matter, we have shown that the solution admits a process of gravitational collapse, leaving a singularity at the end. This solution has, qualitatively, the same temporal behaviour as the dust collapse in GRT. However, we have also found a second possible solution, representing a bounce behavior that is not found in GRT.
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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 cosmological solutions from this theory with their counterparts of General Relativity (Friedmann cosmology). At early times, the Horava- Lifshitz cosmology contains a curvature-dependent dominant term which is stiff matter-reminiscent and this fact motivates to discuss, in some detail, this term beside the usual stiff matter component (pressure=density) if we are thinking in the role that this fluid could have played early in the framework of the holographic cosmology. Nevertheless, we show that an early stiff matter component is of little relevance in Horava-Lifshitz cosmology.
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 $|1-sqrt{beta}|<(10^{-19}-10^{-18})$.
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 dimensionless parameters $alpha$, $beta$ and $lambda$. The first two of these parameters are tightly bound by solar system and gravitational wave propagation experiments, but $lambda$ remains relatively unconstrained ($0leqlambdalesssim 0.01-0.1$). We restrict here to the parameter space region defined by $alpha=beta=0$ (with $lambda$ kept generic), which in a previous paper we showed to be the only one where black hole solutions are non-pathological at the universal horizon, and we focus on possible violations of the strong equivalence principle in systems involving neutron stars. We compute neutron star sensitivities, which parametrize violations of the strong equivalence principle at the leading post-Newtonian order, and find that they vanish identically, like in the black hole case, for $alpha=beta=0$ and generic $lambda eq0$. This implies that no violations of the strong equivalence principle (neither in the conservative sector nor in gravitational wave fluxes) can occur at the leading post-Newtonian order in binaries of compact objects, and that data from binary pulsars and gravitational interferometers are unlikely to further constrain $lambda$.
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 strings are solutions in Hov{r}ava-Lifshitz gravity as well. The geometry is warped in the same way as in Einstein gravity, but the conformal lapse function is not constrained in Hov{r}ava-Lifshitz gravity. It turns out that if $lambda e 1$, there exist no other solutions. For the value of model parameter with which Einstein gravity recovers in IR limit (i.e., $lambda=1$), there exists an additional solution of which the conformal lapse function is determined. Interestingly, this solution admits a uniform BTZ black string along the string direction, which is distinguished from the warped BTZ black string in Einstein gravity. Therefore, it is a good candidate for the test of the theory.
We study the dynamical evolution of a massless scalar perturbation in the Hov{r}ava-Lifshitz black-hole spacetimes with the coupling constants $lambda={1/3}$, $lambda={1/2}$ and $lambda=3$, respectively. Our calculation shows that, for the three cases, the scalar perturbations decay without any oscillation in which the decay rate imprints the parameter of the Hov{r}ava-Lifshitz black hole. The results are quite different from those in the Schwarzschild AdS black hole and can help us understand more about the Hov{r}ava-Lifshitz gravity.
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