Application of Riemann-Hilbert Techniques To Problems Involving Stationary Axisymmetric Perfect Fluid Sources

*9800091ErnstNeugebauer和Meinel最近发现了与刚性旋转的尘埃圆盘相对应的定常轴对称爱因斯坦场方程组的精确整体解，这重新引起了人们对解决与旋转完美流体体有关的问题的兴趣。Ernst博士和Hauser博士将把他们的齐次Hilbert问题(HHP)技术应用于考虑固定轴对称自旋源的匹配问题。为了确定牛顿理论中旋转的齐次Maclaurin椭球的一些有用的相对论模拟，Ernst博士和Hauser博士将研究在某些约束条件下流体解的变化(例如，保持一定的状态方程)。特别是，他们将研究那些保持渐近平坦且无奇点的外部解的存在的变量。

***9800091ErnstThe recent discovery by Neugebauer and Meinel of an exact global solution of the stationary axisymmetric Einstein field equations corresponding to a rigidly rotating disk of dust has created renewed interest in solving problems related to spinning perfect fluid bodies. Dr. Ernst and Dr. Hauser will apply their homogeneous Hilbert problem (HHP) technology to the matching problem to which consideration of stationary axisymmetric spinning sources gives rise.With the objective of identifying some useful relativistic analog of the rotating homogeneous Maclaurin ellipsoids of Newtonian theory, Dr. Ernst and Dr. Hauser will investigate the variation of the fluid solutions with certain constraints [e.g., maintaining a certain equation of state]. In particular, they will investigate those variations that preserve the existence of an exterior solution that is asymptotically flat and singularity-free.***