From Maximal Force to the Field Equations of General Relativity

Abstract

We point out that field equations of general relativity are implied by a maximal force given by c4/4G, analogous to the way that special relativity is implied by a maximal speed given by c. We present some of the arguments for this equivalence. The maxi-mal force naturally plays the role of an elastic constant for space-time. Implications of the maximal force for gravitational wave measurements, cosmology and black holes are highlighted. Quantum aspects of the maximal force are discussed.

From maximum force to physics in 9 lines -- and implications for quantum gravity

“…The maximum value is realized on black hole horizon. At that time, it also became clear that the field equations of general relativity can be deduced from the invariant maximum force c 4 /4G [15,16,32,33,39]. The maximum force value c 4 /4G is due to the maximum energy per distance ratio appearing in general relativity.…”

“…In fact, maximum force c 4 /4G implies Einstein's field equations of general relativity. There are at least two ways to deduce the field equations from maximum force [15,16,32,33,39]. Maximum force also implies the cosmological constant term, but does not fix its value.…”

Tests For Maximum Force and Maximum Power

“…Vacuum elasticity suggests a simple heuristic way to reach the field equations of general relativity starting from maximum force [32]. The energy density ε in vac-uum is a force per area.…”

“…This form of the field equations does not yet incorporate the cosmological constant; but it can be extended to do so [32]. In short, using a line of reasoning inspired by vacuum elasticity, the field equations can be intuitively deduced from maximum force.…”