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Abstract
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In this paper, we present two new families of spatially homogeneous black hole solution for z = 4 Hoˇrava-
Lifshitz Gravity equations in (4 + 1) dimensions with general coupling constant λ and the especial case
λ = 1, considering β = −1/3. The three-dimensional horizons are considered to have Bianchi types II
and III symmetries, and hence the horizons are modeled on two types of Thurston 3-geometries, namely
the Nil geometry and H2 × R. Being foliated by compact 3-manifolds, the horizons are neither spherical,
hyperbolic, nor toroidal, and therefore are not of the previously studied topological black hole solutions in
Hoˇrava-Lifshitz gravity. Using the Hamiltonian formalism, we establish the conventional thermodynamics
of the solutions defining the mass and entropy of the black hole solutions for several classes of solutions.
It turned out that for both horizon geometries the area term in the entropy receives two non-logarithmic
negative corrections proportional to Hoˇrava-Lifshitz parameters. Also, we show that choosing some proper
set of parameters the solutions can exhibit locally stable or unstable behavior.
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