On the Z= 4 Hor̂ava-Lifshitz Gravity

We consider z = 4 Hoava-Lifshitz gravity in both 3+1 and 4+1 dimensions. We find black hole solutions in the IR region for a kind of z = 4 Hoava-Lifshitz gravity which is inherited from the new massive gravity in three dimensions and an analog of the new massive gravity in four dimensions through the quantum inheritance principle. We analyze thermodynamic properties for the black hole solutions for z = 4 Hoava-Lifshitz gravity. We also write out the Friedmann equation in 3+1 dimensions for cosmological solutions.