Rotating metrics admitting non-perfect fluids
Rotating metrics admitting non-perfect fluids
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允许非完美流体的旋转度量
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发表时间：
2004
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通讯作者：
N. Ibohal
中科院分区：
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作者：
N. Ibohal
本文讨论了Newman-Janis算法在函数M（u，r）和e（u，r）的球对称度量中的应用。在通过该算法变换度量之后，这两个函数M（u，r）和e（u，r）将被变换为依赖于三个变量u，r，θ。利用这些三元函数，从Cartan结构方程出发，计算了所有的Newman-Penrose（NP）自旋系数、Ricci标量和Weyl标量。利用这些NP量，我们首先给出了爱因斯坦场方程的旋转解，如Kerr-Newman，旋转Vaidya解和旋转Vaidya-Bonnor解的例子。发现Wang和Wu提出的方法可以用来给出更多的嵌入旋转解的例子，旋转Kerr-Newman解可以与旋转Vaidya解光滑地结合，得到场方程的Kerr-Newman-Vaidya解，同样，也可以得到场方程的Kerr-Newman-Vaidya-Bonnor解.本文还证明了嵌入宇宙如Kerr-Newman-de Sitter、旋转Vaidya-Bonnor-de Sitter、Kerr-Newman-Vaidya-de Sitter等都可以从具有Wang-Wu函数的一般解中导出。所有的旋转嵌入解都可以写成Kerr-Schild形式，这是Xanthopoulos定理的推广。我们还发现所有的旋转解都允许非理想流体。
In this paper an application of Newman-Janis algorithm in spherically symmetric metrics with the functions M(u,r) and e(u,r) has been discussed. After the transformation of the metric via this algorithm, these two functions M(u,r) and e(u,r) will be transformed to depend on the three variables u,r,θ. With these functions of three variables, all the Newman–Penrose (NP) spin coefficients, the Ricci as well as the Weyl scalars have been calculated from the Cartan’s structure equations. Using these NP quantities, we first give examples of rotating solutions of Einstein’s field equations like Kerr–Newman, rotating Vaidya solution and rotating Vaidya–Bonnor solution. It is found that the technique developed by Wang and Wu can be used to give further examples of embedded rotating solutions, that the rotating Kerr–Newman solution can be combined smoothly with the rotating Vaidya solution to derive the Kerr–Newman–Vaidya solution, and similarly, Kerr–Newman–Vaidya–Bonnor solution of the field equations. It has also shown that the embedded universes like Kerr–Newman de Sitter, rotating Vaidya–Bonnor–de Sitter, Kerr–Newman–Vaidya–de Sitter can be derived from the general solutions with Wang–Wu function. All rotating embedded solutions derived here can be written in Kerr–Schild forms, showing the extension of Xanthopoulos’s theorem. It is also found that all the rotating solutions admit non-perfect fluids.