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 $\mathcal{F}\le c^4\mathrm{/}4G$. In the present compact paper we explicitly prove, using the non-linearly coupled Einstein-matter field equations, that the force function $\mathcal{F}\equiv 4\pi r^{2}p(r)$ in {\it stable} self-gravitating horizonless matter configurations is characterized by the upper bound $\mathcal{F}\le c^4\mathrm{/}G$ [here $p(r)$ is the radial pressure inside the self-gravitating matter configuration].