Counterexamples to the Maximum Force Conjecture

Dimensional analysis shows that the speed of light and Newton’s constant of gravitation can be combined to define a quantity $F_{*}=c^4/G_N$ with the dimensions of force (equivalently, tension). Then in any physical situation we must have $F_{\mathrm{physical}}=f{F}_{*}$, where the quantity f is some dimensionless function of dimensionless parameters. In many physical situations explicit calculation yields $f=\mathcal{O}\left(1\right)$, and quite often $f\le 1/4$. This has led multiple authors to suggest a (weak or strong) maximum force/maximum tension conjecture. Working within the framework of standard general relativity, we will instead focus on idealized counter-examples to this conjecture, paying particular attention to the extent to which the counter-examples are physically reasonable. The various idealized counter-examples we shall explore strongly suggest that one should not put too much credence into any truly universal maximum force/maximum tension conjecture. Specifically, idealized fluid spheres on the verge of gravitational collapse will generically violate the weak (and strong) maximum force conjectures. If one wishes to retain any truly general notion of “maximum force” then one will have to very carefully specify precisely which forces are to be allowed within the domain of discourse.