We use the nonlinearly coupled Einstein-matter field equations to prove four theorems that bound from above the dimensionless force function $\mathcal{F}=4\pi r^2·p(r)$ 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) $\mathcal{F}\le 2$ for matter fields that satisfy the dominant energy condition and (ii) $\mathcal{F}\le 1$ for matter fields with a nonpositive energy-momentum trace. In addition, for self-gravitating isotropic matter configurations, we derive the stronger upper bounds: (iii) $\mathcal{F}\le 1$ for matter fields that satisfy the dominant energy condition and (iv) $\mathcal{F}\le 1/2$ for matter fields with a nonpositive energy-momentum trace. Our analytically derived results are in accord with the spirit of the maximum force conjecture in general relativity.

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• Gravitation