A Technical Analysis and a No-Go Theorem for Exponential Force Models of Gravity

Both Newton’s theory of gravity and Einstein’s general relativity admit singularities as potential solutions; this prob-lem has motivated researchers to develop alternative frameworks in an attempt to allow only finite solutions. Thebook Beyond Einstein by Gary Warren, PhD, proposes a “hyperfluid” model which can be described as a mediumpermeating all of space and defined mathematically by an exponential function. The author claims the exponentialfunction produces a continuous and differentiable solution as distance approaches zero. A technical analysis of themathematics and physical structure of the hyperfluid was conducted, with particular attention applied to the behaviorof limits, gravitational potential energy, and compatibility with general relativity. Several inconsistencies are iden-tified with the hyperfluid’s gravity model, including symmetry violations, non-vanishing asymptotic limits, and abreakdown of causality due to the absence of a space-time continuum. The derivation of the hyperfluid’s gravitationalpotential energy leads to a no-go theorem which generalizes to a set of exponential force models. While Beyond Ein-stein provides a clear physical picture motivating the construction, the results indicate that the model, as formulated,does not achieve its stated goal of extending beyond general relativity.