标题： 五维相对论中具有类时额外维度的新渐近反德西特解 显示英文标题

标题： New asymptotic Anti-de Sitter solution with a timelike extra dimension in 5D relativity

摘要： 在五维相对论中，通常的四维宇宙学常数由额外维度决定。 如果额外维度是类空的，可以获得正的宇宙学常数$\Lambda$和四维德西特（dS）空间。 在本文中我们提出，如果额外维度是类时的，相反地，负的$\Lambda$将会出现，所诱导的四维空间将是一个渐近反德西特（AdS）空间。 在最小假设下，我们在规范系统中求解卡鲁扎-克莱因方程$R_{AB} = 0$，并得到一般情况下的AdS解。 结果表明，AdS空间是由超面上（膜）的卡鲁扎-克莱因流形自然诱导出来的。 测试粒子的拉格朗日量表明，如果四维度规不依赖于额外维度，运动方程可以是测地线。 因果性得到了很好的尊重，因为它是由一个零的高维区间适当定义的。 在这种五维相对论中，全息原理可以安全使用，因为膜在体中是渐近欧几里得AdS的。 我们还探讨了关于场/算符对应和两点关联函数的一些可能的全息对偶性含义。 显示英文摘要

摘要： In 5D relativity, the usual 4D cosmological constant is determined by the extra dimension. If the extra dimension is spacelike, one can get a positive cosmological constant $\Lambda$ and a 4D de Sitter (dS) space. In this paper we present that, if the extra dimension is timelike oppositely, the negative $\Lambda$ will be emerged and the induced 4D space will be an asymptotic Anti-de Sitter (AdS). Under the minimum assumption, we solve the Kaluza-Klein equation $R_{AB} = 0$ in a canonical system and obtain the AdS solution in a general case. The result shows that an AdS space is induced naturally from a Kaluza-Klein manifold on a hypersurface (brane). The Lagrangian of test particle indicates the equation of motion can be geodesics if the 4D metric is independent of extra dimension. The causality is well respected because it is appropriately defined by a null higher dimensional interval. In this 5D relativity, the holographic principle can be used safely because the brane is asymptotic Euclidean AdS in the bulk. We also explore some possible holographic duality implications about the field/operator correspondence and the two-points correlation functions.