Simple Gravity II: Strong-Field Structure from a Nonlinear Scalar Field

This work presents a nonlinear scalar-field formulation of gravity in which the strong-field regime is derived directly from the field equation without the use of external ansatz or phenomenological regularization. Through an exact field redefinition, the nonlinear vacuum equation reduces to Laplace's equation, allowing a closed-form spherical solution to be obtained analytically. This solution naturally generates key features of compact-object dynamics, including the existence of a photon sphere and an innermost stable circular orbit (ISCO), which emerge as intrinsic consequences of the field's self-interaction. Based on this framework, the orbital dynamics of compact binary systems are derived, including energy balance, frequency evolution, and a complete parametric description of the strong-field chirp. The radiative sector is constructed consistently, yielding explicit expressions for waveform amplitude, phase evolution, and inspiral termination. A concrete observational example is provided, showing that the theory predicts a higher inspiral cutoff frequency compared to the relativistic prediction. This deviation constitutes a clear and testable observational signature in gravitational-wave data. The formulation provides a non-geometric description of gravity while maintaining internal consistency between static, dynamical, and radiative regimes. The domain of validity and current observational status are discussed, positioning the theory as a testable alternative model for strong-field gravitational phenomena.