arXiv 1005.32212010-05-18hep-thgr-qc

流体中膜奇点及其避免

Brane singularities and their avoidance in a fluid bulk

Ignatios Antoniadis, Spiros Cotsakis, Ifigeneia Klaoudatou

备注：: 26 pages, latex

摘要：

利用渐近分裂的方法，对三维体块中3-膜可能的奇异结构和相应的渐近行为进行了分类，其中体块场的内容由理想流体的模拟参数化，其状态方程为介于“压力”$P$和“密度”$ρ$之间的任意状态方程$P=γρ$.在这种与均匀宇宙学的类比中，时间被横截于3-膜的额外坐标所取代，其世界体积可以具有任意的常曲率。结果主要依赖于常数参数$γ$：（i）对于$γ>-1/2$，平坦膜解在有限距离处存在坍缩奇异性，而在弯曲情况下则消失. (ii)对于$γ<-1$，奇异性是不可避免的，它变成了一个平坦膜的大裂缝类型。(iii)对于$-1<γ\le -1/2$，令人惊讶的结果被发现，而弯曲膜的解决方案是奇异的，平坦的膜是不是，打开了可能性的复苏的自调谐建议。

英文摘要：

Using the method of asymptotic splittings, the possible singularity structures and the corresponding asymptotic behavior of a 3-brane in a five-dimensional bulk are classified, in the case where the bulk field content is parametrized by an analog of perfect fluid with an arbitrary equation of state $P=γρ$ between the `pressure' $P$ and the `density' $ρ$. In this analogy with homogeneous cosmologies, the time is replaced by the extra coordinate transverse to the 3-brane, whose world-volume can have an arbitrary constant curvature. The results depend crucially on the constant parameter $γ$: (i) For $γ>-1/2$, the flat brane solution suffers from a collapse singularity at finite distance, that disappears in the curved case. (ii) For $γ<-1$, the singularity cannot be avoided and it becomes of the type big rip for a flat brane. (iii) For $-1<γ\le -1/2$, the surprising result is found that while the curved brane solution is singular, the flat brane is not, opening the possibility for a revival of the self-tuning proposal.

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