Topolgical Charged Black Holes in Generalized Horava-Lifshitz Gravity

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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.