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arXiv 0706.0260gr-qc
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与广义相对论等价的遥平行理论中的带电轴对称解和能量

Charged Axially Symmetric Solution and Energy in Teleparallel Theory Equivalent to General Relativity

Gamal Gergess Lamee Nashed

备注：
15 pages, Latex
发表信息：
Eur.Phys.J.C49:851-857,2007
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摘要：

在广义相对论的遥平行等效体（TEGR）中，得到了一个具有轴对称性的带电精确解。相关度量具有结构函数$G(ξ)=1-ξ^2-2mAξ^3-q^2A^2ξ^4$。结构函数的四阶性质会使计算变得繁琐。利用坐标变换，我们得到一个四元组，它的度规具有可分解形式的结构函数$(1-ξ^2)(1+r_{+}Aξ)(1+r_{-}Aξ)$，其中$r_{\pm}$是Reissner-Nordstr $\ddot{o}$ m时空的视界.这种新形式的优点是，它的根现在写下来是微不足道的。然后，我们研究这个时空的奇点。利用另一种坐标变换，我们得到一个四分体场。它的相关度规产生了Reissner-Nordstr $\ddot{o}$ m黑洞。在用引力能-动量计算这个四元场的能含量时，我们发现结果形式依赖于径向坐标。利用广义相对论的遥平行等价的引力能动量的正则化表达式，我们得到了能量的一致值。

英文摘要：

An exact charged solution with axial symmetry is obtained in the teleparallel equivalent of general relativity (TEGR). The associated metric has the structure function $G(ξ)=1-ξ^2-2mAξ^3-q^2A^2ξ^4$. The fourth order nature of the structure function can make calculations cumbersome. Using a coordinate transformation we get a tetrad whose metric has the structure function in a factorisable form $(1-ξ^2)(1+r_{+}Aξ)(1+r_{-}Aξ)$ with $r_{\pm}$ as the horizons of Reissner-Nordstr$\ddot{o}$m space-time. This new form has the advantage that its roots are now trivial to write down. Then, we study the singularities of this space-time. Using another coordinate transformation, we obtain a tetrad field. Its associated metric yields the Reissner-Nordstr$\ddot{o}$m black hole. In Calculating the energy content of this tetrad field using the gravitational energy-momentum, we find that the resulting form depends on the radial coordinate! Using the regularized expression of the gravitational energy-momentum in the teleparallel equivalent of general relativity we get a consistent value for the energy.

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