静态理想流体的Pant-Sah状态方程
Static perfect fluids with Pant-Sah equations of state
摘要：
我们分析了3参数家庭的精确的，定期的，静态的，球对称的完美流体解决方案的爱因斯坦方程（对应于2参数家庭的状态方程）由于Pant和Sah和“重新发现”Rosquist和本作者。除了Buchdahl解决方案，其中包含作为一个限制的情况下，流体具有有限的半径，并在物理上是现实的适当的参数范围。状态方程的几何特征在于静态切片上的3-度规，与静态Killing向量的范数的任何线性函数的四次幂共形地重新标度，具有常数标量曲率。这种局部性质不需要球对称性;事实上，它简化了我们在这里回顾的Pant-Sah状态方程的渐近平坦解的球对称性的证明。我们还考虑了牛顿理论中的一个模型，具有类似的几何和物理性质，并证明了渐近平坦解的球对称性。
英文摘要：
We analyze the 3-parameter family of exact, regular, static, spherically symmetric perfect fluid solutions of Einstein's equations (corresponding to a 2-parameter family of equations of state) due to Pant and Sah and "rediscovered" by Rosquist and the present author. Except for the Buchdahl solutions which are contained as a limiting case, the fluids have finite radius and are physically realistic for suitable parameter ranges. The equations of state can be characterized geometrically by the property that the 3-metric on the static slices, rescaled conformally with the fourth power of any linear function of the norm of the static Killing vector, has constant scalar curvature. This local property does not require spherical symmetry; in fact it simplifies the the proof of spherical symmetry of asymptotically flat solutions which we recall here for the Pant-Sah equations of state. We also consider a model in Newtonian theory with analogous geometric and physical properties, together with a proof of spherical symmetry of the asymptotically flat solutions.
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