Upper bounds on the force function in spatially regular self-gravitating matter configurations

We use the non-linearly coupled Einstein-matter field equations to prove four theorems that bound from above the dimensionless force function F =4 pi r 2 times 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) F at most 2 for matter fields that satisfy the dominant energy condition, and (ii) F at most 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) F at most 1 for matter fields that satisfy the dominant energy condition, and (iv) F at most 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.