On the z=4 Horava-Lifshitz Gravity
Rong-Gen Cai, Yan Liu, Ya-Wen Sun
TL;DR
This work constructs z=4 Horava-Lifshitz gravity in 3+1 and 4+1 dimensions by leveraging the detailed balance principle and quantum inheritance from three- and four-dimensional massive gravity theories. It identifies IR black hole solutions for special choices of the beta parameter, derives their thermodynamics including an area term with additional logarithmic and inverse-area corrections, and derives a modified Friedmann equation for cosmology in 3+1 dimensions. The results illuminate how higher-derivative HL terms influence horizon structure, temperature, and entropy, while connecting to GMG/NMG-inspired dynamics in the IR. The study also discusses potential links to AdS/CFT and the broader role of quantum inheritance in constructing renormalizable gravity theories, outlining future directions and open questions on stability and holographic interpretations.
Abstract
We consider z=4 Horava-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 Horava-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 Horava-Lifshitz gravity. We also write out the Friedmann equation in 3+1 dimensions for cosmological solutions.