论文标题
在带有真空边界的旋转完美流体产生的轴对称度量上
On the axisymmetric metric generated by a rotating perfect fluid with the vacuum boundary
论文作者
论文摘要
我们考虑了由爱因斯坦 - 欧拉尔方程（即爱因斯坦方程）以及正压完美液体的能量孔张量的固定旋转轴对称指标系数的方程。尽管已知的共同座分级系统中电势的方程式降低了，但我们得出了所谓的零角动量观察者坐标系统中电势的方程系统。我们新地证明了减少系统与爱因斯坦方程式的完整系统之间的等效性。在一个假设下，角速度在密度的支撑下是恒定的。还分析了系统方程的一致性。在这个基本理论上，我们在整个空间上构建了固定的渐近平坦度量，该公平度是由带有真空边界的缓慢旋转紧凑的完美流体产生的。
We consider the equations for the coefficients of stationary rotating axisymmetric metrics governed by the Einstein-Euler equations, that is, the Einstein equations together with the energy-momentum tensor of a barotropic perfect fluid. Although the reduced system of equations for the potentials in the co-rotating co-ordinate system is known, we derive the system of equations for potentials in the so called zero angular momentum observer co-ordinate system. We newly give a proof of the equivalence between the reduced system and the full system of Einstein equations. It is done under the assumption that the angular velocity is constant on the support of the density. Also the consistency of the equations of the system is analyzed. On this basic theory we construct on the whole space the stationary asymptotically flat metric generated by a slowly rotating compactly supported perfect fluid with vacuum boundary.
