arXiv 0906.05692009-06-02gr-qc

用Dirac观测量表示的LTB时空

LTB spacetimes in terms of Dirac observables

K. Giesel, J. Tambornino, T. Thiemann

备注：: 29 pages, no figures
发表信息：: Class.Quant.Grav.27:105013,2010
DOI：: 10.1088/0264-9381/27/10/105013

摘要：

在广义相对论中，狄拉克观测量（即规范不变对象）的构造在技术上比其他规范理论（如标准模型）复杂，因为它的规范群更复杂，与时空的非同构群密切相关。然而，如果狄拉克观测量的泊松代数足够简单，那么用规范非不变量来表示狄拉克观测量的显式和通常繁琐的表达式是无关紧要的。确切地说，这可以通过采用关系形式主义和布朗和库查最初提出的一种特定类型的物质{ \v r}来实现，即无压尘埃场。此外，人们能够推导出一个紧凑的物理哈密顿量，驱动他们的物理时间演化的表达式。由此产生的规范不变的哈密顿系统是由希格斯粒子的尘埃标量场，并有一个无穷多的守恒电荷，迫使戈德斯通玻色子从演化解耦。在以前的出版物中，我们已经表明，明确的宇宙学扰动。在这篇文章中，我们分析了球对称部门的理论，它原来的解决方案是在一对一的对应类Lemaitre-Tolman-Bondi度量。因此，该理论能够恰当地描述依赖于球对称假设的所有引力实验。

英文摘要：

The construction of Dirac observables, that is gauge invariant objects, in General Relativity is technically more complicated than in other gauge theories such as the standard model due to its more complicated gauge group which is closely related to the group of spacetime diffeomorphisms. However, the explicit and usually cumbersome expression of Dirac observables in terms of gauge non invariant quantities is irrelevant if their Poisson algebra is sufficiently simple. Precisely that can be achieved by employing the relational formalism and a specific type of matter proposed originally by Brown and Kucha{\v r}, namely pressureless dust fields. Moreover one is able to derive a compact expression for a physical Hamiltonian that drives their physical time evolution. The resulting gauge invariant Hamiltonian system is obtained by Higgs -- ing the dust scalar fields and has an infinite number of conserved charges which force the Goldstone bosons to decouple from the evolution. In previous publications we have shown that explicitly for cosmological perturbations. In this article we analyse the spherically symmetric sector of the theory and it turns out that the solutions are in one--to--one correspondence with the class of Lemaitre--Tolman--Bondi metrics. Therefore the theory is capable of properly describing the whole class of gravitational experiments that rely on the assumption of spherical symmetry.

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