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arXiv 1603.02569gr-qcastro-ph.COhep-th
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具有幻影宇宙学背景的McVittie时空的测地线

Geodesics of McVittie Spacetime with a Phantom Cosmological Background

Ioannis Antoniou, Leandros Perivolaropoulos

摘要:

我们研究嵌入在各向同性膨胀宇宙学背景(McVittie度规)中的史瓦西时空的测地线。我们专注于束缚粒子测地线的背景下,包括物质和幻影暗能量与恒定的暗能量状态方程参数$w<-1$涉及未来的大撕裂奇点在一个时间$t_{\ast}$。这样的测地线以前已经研究了牛顿近似,并发现导致解离的束缚系统在一个时间$t_{rip}<t_{\ast}$,其中对于固定的背景$w$,取决于一个单一的无量纲参数$\barω_0$有关的角动量和依赖于质量和大小的束缚系统。我们将这种分析扩展到大质量的束缚系统,其中牛顿近似是不合适的,我们比较推导出的解离时间与相应的时间在牛顿近似的上下文中。通过确定有效势最小值在暗能量排斥力作用下消失的时间,我们发现束缚系统的离解时间比牛顿近似的预言要早。然而,对于所有现有的宇宙学束缚系统,这种影响是可以忽略的,只有在假设的束缚极质量($10^{20} M_\odot$)和大($100Mpc$)束缚系统中才变得重要。我们通过测地线方程的显式解验证了这一结果。这一结果是由于排斥幻影暗能量效应和史瓦西时空中众所周知的最内层稳定轨道之间的相互作用。

英文摘要:

We investigate the geodesics of a Schwarzschild spacetime embedded in an isotropic expanding cosmological background (McVittie metric). We focus on bound particle geodesics in a background including matter and phantom dark energy with constant dark energy equation of state parameter $w<-1$ involving a future Big Rip singularity at a time $t_{\ast}$. Such geodesics have been previously studied in the Newtonian approximation and found to lead to dissociation of bound systems at a time $t_{rip}<t_{\ast}$ which for fixed background $w$, depends on a single dimensionless parameter $\barω_0$ related to the angular momentum and depending on the mass and the size of the bound system. We extend this analysis to large massive bound systems where the Newtonian approximation is not appropriate and we compare the derived dissociation time with the corresponding time in the context of the Newtonian approximation. By identifying the time when the effective potential minimum disappears due to the repulsive force of dark energy we find that the dissociation time of bound systems occurs earlier than the prediction of the Newtonian approximation. However, the effect is negligible for all existing cosmological bound systems and it would become important only in hypothetical bound extremely massive ($10^{20} M_\odot$) and large ($100Mpc$) bound systems. We verify this result by explicit solution of the geodesic equations. This result is due to an interplay between the repulsive phantom dark energy effects and the existence of the well known innermost stable orbits of Schwarzschild spacetimes.

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