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arXiv 1002.0062hep-thgr-qcmath.DG
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Horava-Lifshitz引力中的几何流

Geometric flows in Horava-Lifshitz gravity

Ioannis Bakas, Francois Bourliot, Dieter Lust, Marios Petropoulos

摘要:

考虑四维欧氏Horava-Lifshitz引力的瞬子解满足细致平衡条件。它们由科顿张量和里奇张量以及宇宙常数项的某些组合驱动的三维几何流来描述。变形曲率项可以具有竞争行为,导致各种固定点。瞬子内插在任意两个不动点之间,这两个不动点是具有拓扑质量且λ> 0的引力真空,它们的作用是有限的。特别强调的是与SU(2)isometric配置与均匀的,但一般非各向同性Bianchi IX模型几何。在这种情况下,结合Ricci-Cotton流减少到一个自治系统的常微分方程,其性质进行了详细研究,为不同的耦合。解析地研究了各向同性和各向异性不动点的存在性和稳定性,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R × S^3完备空间。对高维引力的推广也进行了简要的讨论。

英文摘要:

We consider instanton solutions of Euclidean Horava-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 Lambda > 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 globally R x S^3 and complete spaces. Generalizations to higher-dimensional gravities are also briefly discussed.

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