The fluid ball conjecture states that a static perfect fluid space-time is spherically symmetric. In this paper we construct a Robinson’s divergence formula for the static perfect fluid space-time. Inspired by this conjecture, a rigidity result for the spatial factor of a static perfect fluid space-time satisfying some boundary conditions is proved, provided that an equation of state holds.

中文翻译：

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关于流体球猜想

流体球猜想指出，静态的完美流体时空是球对称的。在本文中，我们构建了静态完美流体时空的罗宾逊散度公式。受此猜想的启发，在状态方程成立的情况下，证明了满足某些边界条件的静态完美流体时空的空间因子的刚性结果。