AI 中文总结
该研究利用非线性耦合方程证明关于球对称自引力物质构型中无量纲力函数${\cal F}$的四个定理，给出一般及各向同性物质构型在不同条件下${\cal F}$的上界，结果符合广义相对论最大力猜想。
AI 中文摘要
我们使用非线性耦合的爱因斯坦-物质场方程证明了四个定理，这些定理给出了球对称自引力物质构型的空间正则弯曲时空中无量纲力函数${\cal F}=4\pi r^2\cdot p(r)$（其中$p(r)$是空间正则物质构型内部的径向压力）的上界。具体而言，对于一般（不一定各向同性）物质构型，证明了：（i）满足主导能量条件的物质场${\cal F}\leq 2$；（ii）能量-动量迹非正的物质场${\cal F}\leq 1$。此外，对于自引力各向同性物质构型，得出更强的上界：（iii）满足主导能量条件的物质场${\cal F}\leq 1$；（iv）能量-动量迹非正的物质场${\cal F}\leq 1/2$。我们的解析结果符合广义相对论中最大力猜想的精神。
英文摘要
We use the non-linearly coupled Einstein-matter field equations to prove four theorems that bound from above the dimensionless force function ${\cal F}=4πr^2\cdot p(r)$ in spatially regular curved spacetimes of spherically symmetric self-gravitating matter configurations [here $p(r)$ is the radially-dependent pressure inside the spatially regular matter configurations]. In particular, for generic (not necessarily isotropic) matter configurations it is proved that: (i) ${\cal F}\leq 2$ for matter fields that satisfy the dominant energy condition, and (ii) ${\cal F}\leq 1$ for matter fields with a non-positive energy-momentum trace. In addition, for self-gravitating isotropic matter configurations we derive the stronger upper bounds: (iii) ${\cal F}\leq 1$ for matter fields that satisfy the dominant energy condition, and (iv) ${\cal F}\leq 1/2$ for matter fields with a non-positive energy-momentum trace. Our analytically derived results are in accord with the spirit of the maximum force conjecture in general relativity.
Comments5 pages
Journal refPhysical Review D 113, 124078 (2026)
