AI 中文总结
该研究将广义相对论中理想流体静态球对称时空的精确解拓展至Rastall理论，推导得出对应广义相对论已知情形的解，且w≠1/3、-1时解的行为随常数选择变化。
AI 中文摘要
在广义相对论中，仅当状态方程参数w取0、-1/6、-1/5、-1/3、-1时，具有理想流体且状态方程为p(r)=wρ(r)的静态球对称时空的精确刘维尔解是已知的。我们将该情形拓展至Rastall理论，给出Rastall参数与常数w的关系，并推导得出对应广义相对论中已知情形（除w=-1/6外）的精确解。此外，我们发现当w≠1/3、-1时，存在数类解，其行为随常数选择的不同而变化。
英文摘要
In general relativity, exact Liouvillian solutions for a static and spherically symmetric spacetime with a perfect fluid and the equation of state $p(r)=wρ(r)$ are known only for $w=0,-\frac{1}{6}, -\frac{1}{5}, -\frac{1}{3}, -1$. We extend this setup to Rastall's theory, presenting the relation between the Rastall parameter and the constant $w$, and deriving exact solutions that correspond to the known counterparts in general relativity, except for $w=-\frac{1}{6}$. Furthermore, we find that, when $w\neq \frac{1}{3}, -1$, there exist several types of solutions whose behavior changes depending on the choice of constants.
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