arXiv 0811.08772008-11gr-qcastro-phhep-th

来自空的卡鲁扎-克莱因时空的四维暗能量和物质

Dark Energy and Matter in 4 Dimensions From an Empty Kaluza-Klein Spacetime

M. H. Dehghani, Sh. Assyyaee

备注：: 11 pages, two figures
发表信息：: Phys.Lett.B676:16-20,2009
DOI：: 10.1016/j.physletb.2009.04.056

摘要：

本文研究了空的$n(\geq 8)$维Kaluza-Klein时空$\mathcal{M}^{4}\times \mathcal{K}^{n-4}$中不含宇宙学常数项的三阶Lovelock方程，其中$\mathcal{K}^{n-4}$是常曲率空间.我们证明了高维时空的空性对四维时空$\mathcal{M}^{4}$的度规函数施加了一个约束。我们在黑洞物理学的背景下考虑这个约束方程的影响，并在没有物质场和宇宙学常数（暗能量）的情况下找到了一个四维黑洞解。该解与文献[H. Maeda和N. Dadhich，Phys. Rev. D 74（2006）021501（R）]，从而证明了在高维Kaluza-Klein时空中满足真空Lovelock方程的$\mathcal{M}^{4}$度规是唯一的.这个黑洞解表明，空的高维卡鲁扎-克莱因时空的曲率产生了暗能量和四维中具有非无痕能量-动量张量的物质。

英文摘要：

We consider the third order Lovelock equations without the cosmological constant term in an empty $n(\geq 8)$-dimensional Kaluza-Klein spacetime $\mathcal{M}^{4}\times \mathcal{K}^{n-4}$, where $\mathcal{K}^{n-4}$ is a constant curvature space. We show that the emptiness of the higher-dimensional spacetime imposes a constraint on the metric function(s) of 4-dimensional spacetime $\mathcal{M}^{4}$. We consider the effects of this constraint equation in the context of black hole physics, and find a black hole solution in 4 dimensions in the absence of matter field and the cosmological constant (dark energy). This solution has the same form as the 4-dimensional solution introduced in [H. Maeda and N. Dadhich, Phys. Rev. D 74 (2006) 021501(R)] for Gauss-Bonnet gravity in the presence of cosmological constant, and therefore the metric of $\mathcal{M}^{4}$ which satisfies the vacuum Lovelock equations in higher-dimensional Kaluza-Klein spacetime is unique. This black hole solution shows that the curvature of an empty higher-dimensional Kaluza-Klein spacetime creates dark energy and matter with non-traceless energy-momentum tensor in 4 dimensions.

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