具有Nil几何和$H^2\times R$视界的$(4+1)$ Hoenava-Lifshitz引力空间均匀黑洞解
Spatially homogeneous black hole solutions in $z=4$ Hořava-Lifshitz gravity in $(4+1)$ dimensions with Nil geometry and $H^2\times R$ horizons
摘要：
本文给出了具有一般耦合常数$λ$和特殊情形$λ=1$（考虑$β=-1/3$）的$(4+1)$维中的$z=4$ Hoenava-Lifshitz引力方程的两类新的空间齐次黑洞解.三维层位被认为具有Bianchi型$II$和$III$对称性，因此层位被建模为两种类型的Thurston $3$几何，即Nil几何和$H^2\times R$。由于视界是由紧致三维流形构成的，因此它既不是球面的，也不是双曲的，也不是环面的，因此它不是以前研究过的在Hoenava-Lifshitz引力下的拓扑黑洞解.利用哈密顿形式，我们建立了定义了几类解的黑洞解的质量和熵的解的传统热力学。事实证明，对于两种视界几何形状，熵中的面积项都受到两个与霍瓦瓦-利夫希茨参数成比例的非对数负修正。我们还证明了，选择适当的参数，解可以表现出局部稳定或不稳定的行为。
英文摘要：
In this paper, we present two new families of spatially homogeneous black hole solution for $z=4$ Hořava-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 $H^2\times R$. 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 Hořava-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 Hořava-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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