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arXiv 0909.4127hep-th
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可投射条件下修正Horava-Lifshitz引力的静态球对称解

Static Spherically Symmetric Solutions to modified Horava-Lifshitz Gravity with Projectability Condition

Jin-Zhang Tang, Bin Chen

摘要:

本文在可投射条件下求Horava-Lifshitz类引力的静态球对称解。我们考虑没有细致平衡的引力作用的最一般形式,并要求时空度规遵守可投射性条件。我们发现,对于任意的$λ$值,都可能存在拓扑$R\times M_3$的解,其中$R$是时间方向,$M_3$是一个依赖于宇宙学常数和作用势的三维最大对称空间.此外,在紫外区,当$λ\neq 1$为正解时,我们发现了Minkowski或de-Sitter时空解,而在红外区,当$λ=1$为负解时,我们证明了(dS-)Schwarzschild解是唯一的非平凡解.我们还注意到,文献中找到的其他静态球对称解不满足可投射条件,也不是我们得到的解。我们的研究表明,在具有可投射条件的Horava-Lifshitz引力中,在太阳系实验中,对爱因斯坦的广义相对论没有新的修正。

英文摘要:

In this paper we seek static spherically symmetric solutions of Horava-Lifshitz-like gravity with projectability condition. We consider the most general form of gravity action without detailed balance, and require the spacetime metric to respect the projectability condition. We find that for any value of $λ$, it may exists the solutions of topology $R\times M_3$, where $R$ is the time direction and $M_3$ is a three-dimensional maximally symmetric space depending on the value of cosmological constant and the potential of the action. Besides, in the UV region where $λ\neq 1$, we find Minkowski or de-Sitter space-time as the solution, while in the IR region where $λ=1$, we prove that (dS-)Schwarzschild solution is the only nontrivial solution. We also notice that the other static spherically symmetric solutions found in the literature do not satisfy the projectability condition and are not the solutions we get. Our study shows that in Horava-Lifshitz gravity with projectability condition, there is no novel correction to Einstein's general relativity in solar system tests.

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