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arXiv 0705.3380hep-thgr-qc
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Lorentzian和Signature Changing膜

Lorentzian and signature changing branes

Marc Mars, José M. M. Senovilla, Raül Vera

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23 pages, 2 figures
发表信息：
Phys.Rev.D76:044029,2007
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摘要：

一般超曲面层被认为是为了描述膜世界和壳宇宙学。对超曲面的因果性质没有限制，因此超曲面可能具有内部签名变化。加强我们在前一封信[1]中的结果，我们确认在这些膜/壳场景中实现了对签名变化的良好，规则和一致的描述，同时保持超曲面和体完全规则。我们的形式主义允许一个统一的描述传统的类时膜/壳连同签名改变，或纯零，的。这允许对两种情况下的结果进行详细比较。应用程序的情况下，超表面层在静态散装，导致一般罗伯逊-沃克几何的层-与可能的签名变化。明确的例子反德西特散装研究。在不同的设置（$Z_{2}$ -镜像膜，不对称壳，签名改变膜）的允许的行为进行了详细分析。我们特别表明，（i）在非对称壳层中，能量密度存在一个上限，（ii）当接近签名的变化时，膜内的能量密度消失。被认为是从膜内看到的一个“奇点”的签名变化的描述。我们还发现了膜/壳的基本常数之间的新关系，它的张力，宇宙学和引力常量的体积，独立的存在与否的变化的签名。

英文摘要：

General hypersurface layers are considered in order to describe brane-worlds and shell cosmologies. No restriction is placed on the causal character of the hypersurface which may thus have internal changes of signature. Strengthening the results in our previous letter [1], we confirm that a good, regular and consistent description of signature change is achieved in these brane/shells scenarios, while keeping the hypersurface and the bulk completely regular. Our formalism allows for a unified description of the traditional timelike branes/shells together with the signature-changing, or pure null, ones. This allows for a detailed comparison of the results in both situations. An application to the case of hypersurface layers in static bulks is presented, leading to the general Robertson-Walker geometry on the layer --with a possible signature change. Explicit examples on anti de Sitter bulks are then studied. The permitted behaviours in different settings ($Z_{2}$-mirror branes, asymmetric shells, signature-changing branes) are analysed in detail. We show in particular that (i) in asymmetric shells there is an upper bound for the energy density, and (ii) that the energy density within the brane vanishes when approaching a change of signature. The description of a signature change as a `singularity' seen from within the brane is considered. We also find new relations between the fundamental constants in the brane/shell, its tension, and the cosmological and gravitational constants of the bulk, independently of the existence or not of a change of signature.

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