具有内缘的相对论性静态薄尘埃盘：新精确解的无限族
Relativistic static thin dust disks with an inner edge: An infinite family of new exact solutions
摘要：
本文给出了静态轴对称时空中爱因斯坦真空方程的一个新的精确解的无限族。所有的度量函数的解决方案显式计算和获得的表达式是简单地写在扁球坐标。此外，解是渐近平坦的，处处正则，因为它是通过计算所有的曲率标量。这些解描述了一个具有中心内缘的薄尘埃盘的无限族，其能量密度处处为正且表现良好，其能量-动量张量与所有能量条件完全一致。现在，尽管圆盘是无限延伸的，但它们都有有限的质量。这个家族的第一个成员与史瓦西黑洞的叠加以前曾被提出[G. A. González和A. C. Gutiérrez-Piñeres，arXiv：0811.3002v1（2008）]，而在随后的论文中，将对整个家族的相应叠加进行详细分析。
英文摘要：
An infinite family of new exact solutions of the Einstein vacuum equations for static and axially symmetric spacetimes is presented. All the metric functions of the solutions are explicitly computed and the obtained expressions are simply written in terms of oblate spheroidal coordinates. Furthermore, the solutions are asymptotically flat and regular everywhere, as it is shown by computing all the curvature scalars. These solutions describe an infinite family of thin dust disks with a central inner edge, whose energy densities are everywhere positive and well behaved, in such a way that their energy-momentum tensor are in fully agreement with all the energy conditions. Now, although the disks are of infinite extension, all of them have finite mass. The superposition of the first member of this family with a Schwarzschild black hole was presented previously [G. A. González and A. C. Gutiérrez-Piñeres, arXiv: 0811.3002v1 (2008)], whereas that in a subsequent paper a detailed analysis of the corresponding superposition for the full family will be presented.
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