  Dimensional analysis shows that the speed of light and Newton's constant of
gravitation can be combined to define a quantity $F_* = {c^4\over G_N}$ with
the dimensions of force (equivalently, tension). Then in any physical situation
we must have $F_{physical} = f \; F_*$, where the quantity $f$ is some
dimensionless function of dimensionless parameters. In many physical situations
explicit calculation yields $f= O(1)$, and quite often $f \leq {1\over4}$. This
has lead 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 counter-examples to this conjecture,
paying particular attention to the extent to which the counter-examples are
physically reasonable. The various counter-examples we shall explore strongly
suggest that one should not put too much credence into any universal maximum
force/maximum tension conjecture. Specifically, fluid spheres on the verge of
gravitational collapse will generically violate the weak (and strong) maximum
force conjectures. If one wishes to retain any 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.
