Maximum force conjecture in curved spacetimes of stable self-gravitating matter configurations

Gibbons and Schiller have raised the physically interesting conjecture that forces in general relativity are bounded from above by the mathematically compact relation ${\cal F}\leq c^4/4G$. In the present compact paper we explicitly prove, using the non-linearly coupled Einstein-matter field equations, that the force function ${\cal F}\equiv 4\pi r^2 p(r)$ in {\it stable} self-gravitating horizonless matter configurations is characterized by the upper bound ${\cal F}\leq c^4/G$ [here $p(r)$ is the radial pressure inside the self-gravitating matter configuration].