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An approximate global solution of Einstein's equations for a finite body

机译:有限体的爱因斯坦方程的近似全局解

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摘要

We obtain an approximate global stationary and axisymmetric solution ofEinstein's equations which can be considered as a simple star model: aself-gravitating perfect fluid ball with constant mass density rotating inrigid motion. Using the post-Minkowskian formalism (weak-field approximation)and considering rotation as a perturbation (slow-rotation approximation), wefind approximate interior and exterior (asymptotically flat) solutions to thisproblem in harmonic and quo-harmonic coordinates. In both cases, interior andexterior solutions are matched, in the sense of Lichnerowicz, on the surface ofzero pressure to obtain a global solution. The resulting metric depends onthree arbitrary constants: mass density, rotational velocity and the starradius at the non-rotation limit. The mass, angular momentum, quadrupole momentand other constants of the exterior metric are determined by these threeparameters. It is easy to show that this type of fluid cannot be a source ofthe Kerr metric
机译:我们获得了爱因斯坦方程组的近似整体平稳和轴对称解,可以将其视为简单的星形模型:具有恒定质量密度旋转惯性运动的自引力完美流体球。使用后Minkowskian形式主义(弱场近似)并将旋转视为扰动(慢旋转近似),我们以谐波和准谐波坐标的形式对此问题找到了近似的内部和外部(渐近平坦)解。在Lichnerowicz的意义上,在两种情况下,内部和外部解决方案都在零压力的表面上匹配,以获得整体解决方案。所得的度量取决于三个任意常数:非旋转极限处的质量密度,旋转速度和星半径。外部度量的质量,角动量,四极矩和其他常数由这三个参数确定。容易证明这种类型的流体不能成为克尔度量的来源

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