arXiv 0905.27862009-05gr-qc

Horava-Lifshitz时空中的类时测地运动

Timelike Geodesic Motion in Horava-Lifshitz Spacetime

Juhua Chen, Yongjiu Wang

备注：: 12 pages, 4 figures. accepted by IJMPA
发表信息：: Int.J.Mod.Phys.A25:1439-1448,2010
DOI：: 10.1142/S0217751X10048962

摘要：

最近，Ho $\breve{r}$等人提出了一个非相对论性的引力重整化理论。当被限制为满足细致平衡的条件时，这个理论与三维的拓扑大质量引力和科顿张量的几何密切相关。在长距离上，这个理论预计会流到相对论值$λ= 1$，因此可以作为爱因斯坦广义相对论的紫外补充或其红外修正的可能候选者。本文在允许时滞函数依赖于空间坐标$x^i$和$t$的条件下，得到了球对称解.然后通过分析粒子有效势的行为，研究了Ho $\breve{r}$ ava-Lifshitz时空中粒子的类时测地线运动.我们发现，当非径向粒子的能量在适当的范围内时，非径向粒子沿着类时测地线从有限距离处落向中心。然而，我们发现径向粒子沿类时测地线的运动是复杂的。由于径向粒子的能量不同，有以下几种情况：1）当径向粒子的能量大于一个临界值$E_{C}$时，粒子将直接从无穷远落向奇点; 2）当径向粒子能量等于临界值$E_{C}$时，粒子轨道在$r=r_{C}$处不稳定，即粒子将从$r=r_{C}$逃逸到无穷远或奇点，这由粒子的初始条件决定; 3）当径向粒子的能量在一定范围内时，粒子会从无穷远反弹到无穷远或坠入奇点，这也由粒子的初始条件决定。

英文摘要：

Recently Ho$\breve{r}$ava proposed a non-relativistic renormalisable theory of gravitation. When restricted to satisfy the condition of detailed balance, this theory is intimately related to topologically massive gravity in three dimensions, and the geometry of the Cotton tensor. At long distances, this theory is expected to flow to the relativistic value $λ= 1$, and could therefore serve as a possible candidate for a UV completion of Einstein general relativity or an infrared modification thereof. In this paper under allowing the lapse function to depend on the spatial coordinates $x^i$ as well as $t$, we obtain the spherically symmetric solutions. And then by analyzing the behavior of the effective potential for the particle, we investigate the timelike geodesic motion of particle in the Ho$\breve{r}$ava-Lifshitz spacetime. We find that the nonradial particle falls from a finite distance to the center along the timelike geodesics when its energy is in an appropriate range. However, we find that it is complexity for radial particle along the timelike geodesics. There are follow different cases due to the energy of radial particle: 1) When the energy of radial particle is higher than a critical value $E_{C}$, the particle will fall from infinity to the singularity directly; 2) When the energy of radial particle equals to the critical value $E_{C}$, the particle orbit is unstable at $r=r_{C}$, i.e. the particle will escape from $r=r_{C}$ to the infinity or to the singularity, which is determined by the initial conditions of the particle; 3) When the energy of radial particle is in a proper range, the particle will rebound to the infinity or plunge to the singularity from a infinite distance, which is also determined by the initial conditions of the particle.

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摘要：

英文摘要：

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