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arXiv 0908.1322gr-qc
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球形虫洞有效势的结构

On the Structure of the Effective Potential for a Spherical Wormhole

N. Montelongo Garcia, T. Zannias

摘要:

分析了任意球形虫洞喉道附近描述因果测地线的有效势$V$的结构。爱因斯坦方程相对于一组覆盖喉附近的常规坐标意味着任何球形虫洞可以从喉作为初始值表面的有效初始值问题的解决方案构建。初始数据包括物质变量、喉道面积A(0)和喉道上的红移因子梯度$Λ(0)$。每当$Λ(0)=0$,有效电位$V$在喉部有一个临界点。条件的数据导出,确保临界点是一个局部最小值(分别)。最大值)。对于特定的类史瓦西虫洞,$V$在喉道上表现出与测试粒子的能量$E$和角动量$L^2 $无关的局部最小值,因此这种虫洞在喉道上允许稳定的圆形类时和零测地线。对于Chaubergin虫洞的家庭,我们表明,这样的测地线是不稳定的。基于度规的幂级数表示,得到了远离喉道的$V$的一些性质,这些性质对于分析球形虫洞喉道附近的吸积盘和辐射过程是有用的.

英文摘要:

The structure of the effective potential $V$ describing causal geodesics near the throat of an arbitrary spherical wormhole is analyzed. Einstein's equations relative to a set of regular coordinates covering a vicinity of the throat imply that any spherical wormhole can be constructed from solutions of an effective initial value problem with the throat serving as an initial value surface. The initial data involve matter variables, the area A(0) of the throat and the gradient $Λ(0)$ of the red shift factor on the throat. Whenever $Λ(0)=0$, the effective potential $V$ has a critical point on the throat. Conditions upon the data are derived ensuring that the critical point is a local minimum (resp. maximum). For particular families of Quasi-Schwarzschild wormholes, $V$ exhibits a local minimum on the throat independently upon the energy $E$ and angular momentum $L^2 $ of the test particles and thus such wormholes admit stable circular timelike and null geodesics on the throat. For families of Chaplygin wormholes, we show that such geodesics are unstable. Based on a suitable power series representation of the metric, properties of $V$ away from the throat are obtained that are useful for the analysis of accretion disks and radiation processes near the throat of any spherical wormhole.

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