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arXiv 1202.4915hep-th
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关于multi-M2膜层的光滑性

On the smoothness of multi-M2 brane horizons

Chethan N. Gowdigere, Siddharth Satpathy, Yogesh K. Srivastava

摘要:

我们计算了多个$M2$膜解的水平光滑度,其中膜沿公共轴。我们发现,度量一般只有三次连续可微的任何地平线。四种形式的场强被发现是只有两次连续可微。我们的工作与高斯零类坐标,这是通过求解多$M2$膜几何的测地线方程。我们还发现不同的,确切的坐标变换,采取度量从各向同性坐标中的度量是三次可微的地平线。这两种方法给出了相同的结果,即多$M2$膜度规在视界上只能连续可微三次。

英文摘要:

We calculate the degree of horizon smoothness of multi- $M2$-brane solution with branes along a common axis. We find that the metric is generically only thrice continuously differentiable at any of the horizons. The four-form field strength is found to be only twice continuously differentiable. We work with Gaussian null-like co-ordinates which are obtained by solving geodesic equations for multi-$M2$ brane geometry. We also find different, exact co-ordinate transformations which take the metric from isotropic co-ordinates to co-ordinates in which metric is thrice differentiable at the horizon. Both methods give the same result that the multi-$M2$ brane metric is only thrice continuously differentiable at the horizon.

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