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arXiv 1105.4259hep-thastro-ph.COgr-qchep-ph
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Horava-Lifshitz理论中球时空的黑洞和整体结构

Black holes and global structures of spherical spacetimes in Horava-Lifshitz theory

Jared Greenwald, Jonatan Lenells, J. X. Lu, V. H. Satheeshkumar, Anzhong Wang

备注：
latex4, 15 figures. Some typos were corrected
发表信息：
Phys. Rev. D84, 084040 (2011)
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摘要：

本文采用运动学方法系统地研究了Horava-Lifshitz（HL）理论中的黑洞。由于非相对论色散关系，光速是无限的，测试粒子不遵循测地线。因此，广义相对论和HL理论在因果结构和黑洞方面存在显著差异。特别地，视界半径一般依赖于测试粒子的能量。将它们应用于最近在非相对论性广义协变引力理论中发现的球形静态真空解，我们发现，对于具有足够高能量的测试粒子，视界的半径可以尽可能地小，尽管奇点原则上只能由具有无限高能量的观察者看到。在这些研究中，我们特别注意的整体结构的解决方案，并发现，由于叶理保持-同态对称性，${Diff}(M,{\cal{F}})$，他们是相当不同的相应的GR，即使解决方案是相同的。特别是，${Diff}(M,{\cal{F}})$不允许使用彭罗斯图。在真空解中，有些解产生了爱因斯坦-罗森桥的结构，其中两个渐近平坦的区域由具有有限非零半径的喉部连接。我们还研究了在这样的设置中的慢旋转的解决方案，并获得了所有的解决方案，其特征在于一个任意的功能$A_{0}(r)$。$A_{0} = 0$的情况简化为GR中得到的慢旋转克尔解。

英文摘要：

We systematically study black holes in the Horava-Lifshitz (HL) theory by following the kinematic approach, in which a horizon is defined as the surface at which massless test particles are infinitely redshifted. Because of the nonrelativistic dispersion relations, the speed of light is unlimited, and test particles do not follow geodesics. As a result, there are significant differences in causal structures and black holes between general relativity (GR) and the HL theory. In particular, the horizon radii generically depend on the energies of test particles. Applying them to the spherical static vacuum solutions found recently in the nonrelativistic general covariant theory of gravity, we find that, for test particles with sufficiently high energy, the radius of the horizon can be made as small as desired, although the singularities can be seen in principle only by observers with infinitely high energy. In these studies, we pay particular attention to the global structure of the solutions, and find that, because of the foliation-preserving-diffeomorphism symmetry, ${Diff}(M,{\cal{F}})$, they are quite different from the corresponding ones given in GR, even though the solutions are the same. In particular, the ${Diff}(M,{\cal{F}})$ does not allow Penrose diagrams. Among the vacuum solutions, some give rise to the structure of the Einstein-Rosen bridge, in which two asymptotically flat regions are connected by a throat with a finite non-zero radius. We also study slowly rotating solutions in such a setup, and obtain all the solutions characterized by an arbitrary function $A_{0}(r)$. The case $A_{0} = 0$ reduces to the slowly rotating Kerr solution obtained in GR.

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