Topolgical Charged Black Holes in Generalized Horava-Lifshitz Gravity

Abstract

As a candidate of quantum gravity in ultrahigh energy, the $(3+1)$-dimensional Hořava-Lifshitz (HL) gravity with critical exponent $z\ne 1$, indicates anisotropy between time and space at short distance. In the paper, we investigate the most general $z=d$ Hořava-Lifshitz gravity in arbitrary spatial dimension $d$, with a generic dynamical Ricci flow parameter $\lambda$ and a detailed balance violation parameter $\epsilon$. In arbitrary dimensional generalized HL${}_{d+1}$ gravity with $z\ge d$ at long distance, we study the topological neutral black hole solutions with general $\lambda$ in $z=d$ HL${}_{d+1}$, as well as the topological charged black holes with $\lambda =1$ in $z=d$ HL${}_{d+1}$. The HL gravity in the Lagrangian formulation is adopted, while in the Hamiltonian formulation, it reduces to Dirac$-$De Witt's canonical gravity with $\lambda =1$. In particular, the topological charged black holes in $z=5$ HL${}_6$, $z=4$ HL${}_5$, $z=3,4$ HL${}_4$ and $z=2$ HL${}_3$ with $\lambda =1$ are solved. Their asymptotical behaviors near the infinite boundary and near the horizon are explored respectively. We also study the behavior of the topological black holes in the $(d+1)$-dimensional HL gravity with $U(1)$ gauge field in the zero temperature limit and finite temperature limit, respectively. Thermodynamics of the topological charged black holes with $\lambda =1$, including temperature, entropy, heat capacity, and free energy are evaluated.

51 pages, published version. The theoretical framework of z=d HL gravity is set up, and higher curvature terms in spatial dimension become relevant at UV fixed point. Lovelock term, conformal term, new massive term, and Chern-Simons term with different critical exponent z are studied

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• Thermodynamic Topology of $D=4,5$ Horava Lifshitz Black Hole in Two Ensembles
• Black Hole Evaporation in Hořava-Lifshitz Gravity
• Topological Non-Fermi Liquid
• Phase Transition of the Horava-Lifshitz AdS black holes
• $\lambda$ phase transition in Horava gravity
• Spatially homogeneous black hole solutions in $z=4$ Hořava-Lifshitz gravity in $(4+1)$ dimensions with Nil geometry and $H^2\times R$ horizons