What Does the Central Limit Theorem Have to Say About General Relativity

In this paper, we speculate on a possible connection between the Bayes’s law and the Einstein’s general relativity equation to support the use of a metric based on an erfc gravitational potential that has been recently proposed to provide some cues to open problems in the solar systems. Starting from a basic interdependence premise, an analogy between Einstein’s equation and Bayes’s law is used to analyze the linear case of a weak field static symmetric massive object, providing a probabilistic context that takes into account the probability of presence of a given energy density in its corresponding 4D curved space-time manifold. Using the Central Limit Theorem to model globally the very slow process of star formation and mathematically express the corresponding probability density, the new framework provides a rationale for the emergence of a weighted Newton’s law of gravitation. One key feature of this modified gravity model is that it relies on the existence of an intrinsic emergent physical constant σ, a star-specific proper length that scales all its surroundings.