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As a candidate of quantum gravity in ultrahigh energy, the (3+1)-dimensional Hořava-Lifshitz (HL) gravity with critical exponent z≠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 λ and a detailed balance violation parameter ε. In arbitrary dimensional generalized HLd+1 gravity with z≥d at long distance, we study the topological neutral black hole solutions with general λ in z=d HLd+1, as well as the topological charged black holes with λ=1 in z=d HLd+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 λ=1. In particular, the topological charged black holes in z=5 HL6, z=4 HL5, z=3,4 HL4, and z=2 HL3 with λ=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 λ=1, including temperature, entropy, heat capacity, and free energy are evaluated. [ABSTRACT FROM AUTHOR]

In (2+1)-dimensional hydrodynamic systems with broken parity, the shear and bulk viscosity is joined by the Hall viscosity and curl viscosity. The dual holographic model has been constructed by coupling a pseudoscalar to the gravitational Chern-Simons term in (3+1)-dimensional bulk gravity. In this paper, we investigate the nonrelativistic fluid with Hall viscosity and curl viscosity living on a finite radial cutoff surface in the bulk. Employing the nonrelativistic hydrodynamic expansion method, we obtain the incompressible Navier-Stokes equations with Hall viscosity and curl viscosity. Unlike the shear viscosity, the ratio of the Hall viscosity over entropy density is found to be cutoff scale dependent, and it tends to zero when the cutoff surface approaches the horizon of the background space-time. [ABSTRACT FROM AUTHOR]