Simple Gravity: A Nonlinear Scalar Field Theory of Gravitation

This work presents Simple Gravity, a nonlinear scalar theory of gravitation formulated in flat spacetime. The theory extends the classical Poisson equation by incorporating the energy of the gravitational field as a source term, leading to a self-consistent nonlinear structure. An exact spherically symmetric solution is obtained, recovering Newtonian gravity in the weak-field limit while introducing logarithmic corrections at shorter distances. The formulation includes a consistent Lagrangian for particle dynamics, yielding correct predictions for orbital motion and perihelion precession. Light propagation is described through an effective refractive index, reproducing gravitational lensing, Shapiro time delay, and redshift. A dynamical extension of the field demonstrates that gravitational disturbances propagate at the speed of light. The radiative sector is derived and, with an effective normalization of the field energy, reproduces the quadrupole radiation formula observed in binary systems. The theory provides a non-geometric alternative to gravitation, describing gravitational phenomena through a scalar field without invoking spacetime curvature.