Ernst Equation and Riemann Surfaces: Analytical and Numerical Methods
Ernst Equation and Riemann Surfaces: Analytical and Numerical Methods
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DOI：
10.1007/11540953
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发表时间：
2005-11
期刊：
影响因子：
--
通讯作者：
C. Klein;O. Richter
中科院分区：
文献类型：
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作者：
C. Klein;O. Richter
爱因斯坦方程的精确解在许多方面对理解广义相对论都很有用。它们导致了黑洞和事件视界等物理概念的产生，并有助于形象化该理论的有趣特征。此外，它们还被用来测试各种近似方法和数值代码的质量。最强大的解决方案生成方法是由于可积系统的理论。在轴对称静止时空的情况下，爱因斯坦方程等价于完全可积的恩斯特方程。在这卷的解决方案恩斯特方程与黎曼曲面进行了详细的研究和物理和数学方面的这一类讨论分析和数值。
Exact solutions to Einsteins equations have been useful for the understanding of general relativity in many respects. They have led to physical concepts as black holes and event horizons and helped to visualize interesting features of the theory. In addition they have been used to test the quality of various approximation methods and numerical codes. The most powerful solution generation methods are due to the theory of Integrable Systems. In the case of axisymmetric stationary spacetimes the Einstein equations are equivalent to the completely integrable Ernst equation. In this volume the solutions to the Ernst equation associated to Riemann surfaces are studied in detail and physical and mathematical aspects of this class are discussed both analytically and numerically.