Geometric flows in Hořava-Lifshitz gravity
Geometric flows in Hořava-Lifshitz gravity
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DOI：
10.1007/jhep04(2010)131
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发表时间：
2010-01
影响因子：
5.4
通讯作者：
I. Bakas;F. Bourliot;D. Lüst;M. Petropoulos
中科院分区：
文献类型：
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作者：
I. Bakas;F. Bourliot;D. Lüst;M. Petropoulos
我们考虑了满足详细平衡条件的四维欧几里得HořAVA-Lifshitz引力的瞬时子解。它们是由由Cotton张量和Ricci张量的某些组合以及宇宙常数项驱动的三维几何流动描述的。变形曲率项可以具有竞争行为，从而导致各种固定点。瞬子在任意两个固定点之间进行内插，这两个固定点是具有Λ>；0的拓扑质量引力真空，并且它们的作用是有限的。特别强调了SU(2)等距构型与均匀但一般非各向同性的Bianci IX模型几何构型的关系。在这种情况下，组合的Ricci-Cotton流归结为一个自治的常微分方程组，对不同耦合的性质进行了详细的研究。对各向同性不动点和各向异性不动点的存在性和稳定性进行了解析研究，得到了一些精确解。对相应的瞬子进行了分类，它们都是整体完备的空间。文中还简要讨论了对高维引力的推广。
We consider instanton solutions of Euclidean Hořava-Lifshitz gravity in four dimensions satisfying the detailed balance condition. They are described by geometric flows in three dimensions driven by certain combinations of the Cotton and Ricci tensors as well as the cosmological-constant term. The deformation curvature terms can have competing behavior leading to a variety of fixed points. The instantons interpolate between any two fixed points, which are vacua of topologically massive gravity with Λ> 0, and their action is finite. Special emphasis is placed on configurations with SU (2) isometry associated with homogeneous but generally non-isotropic Bianchi IX model geometries. In this case, the combined Ricci-Cotton flow reduces to an autonomous system of ordinary differential equations whose properties are studied in detail for different couplings. The occurrence and stability of isotropic and anisotropic fixed points are investigated analytically and some exact solutions are obtained. The corresponding instantons are classified and they are all globallyand complete spaces. Generalizations to higher-dimensional gravities are also briey discussed.