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