Maximum force conjecture in curved spacetimes of stable self-gravitating matter configurations

TL;DR

This paper proves that in stable, horizonless self-gravitating matter configurations within general relativity, the force function is bounded above by a specific constant, supporting the maximum force conjecture.

Contribution

It provides a rigorous proof that the force in stable self-gravitating matter configurations is bounded by c^4/G, confirming a conjecture in curved spacetimes.

Findings

Force function bounded by c^4/G in stable configurations

Supports the maximum force conjecture in general relativity

Explicit relation between pressure and force in matter configurations

Abstract

Gibbons and Schiller have raised the physically interesting conjecture that forces in general relativity are bounded from above by the mathematically compact relation ${\cal F}\leq c^4/4G$. In the present compact paper we explicitly prove, using the non-linearly coupled Einstein-matter field equations, that the force function ${\cal F}\equiv 4\pi r^2 p(r)$ in {\it stable} self-gravitating horizonless matter configurations is characterized by the upper bound ${\cal F}\leq c^4/G$ [here $p(r)$ is the radial pressure inside the self-gravitating matter configuration].