Counterexamples to the maximum force conjecture

TL;DR

This paper challenges the maximum force conjecture in general relativity by presenting counterexamples involving fluid spheres near gravitational collapse, suggesting no universal maximum force exists without strict domain restrictions.

Contribution

It provides explicit counterexamples within general relativity that violate the maximum force conjecture, questioning its universality and emphasizing the need for domain-specific constraints.

Findings

Fluid spheres near collapse violate maximum force bounds

Counterexamples cast doubt on the universality of the maximum force conjecture

Careful domain specification is necessary for any maximum force principle

Abstract

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.