A Mathematical Framework for an Emergent Gravity Model

In this paper, we present a mathematical framework for an emergent gravity model, where gravity is not treated as a fundamental force but rather as a dynamic phenomenon arising from local baryon asymmetry (A(t)) and symmetry restoration (R(t)). We derive the governing equations for the time evolution of these variables, analyze their coupled dynamics, and explore the resulting gravitational field. Through numerical simulations and phase space analysis, we investigate the stability, equilibrium states, and long-term behavior of the system. We also extend the model to include velocity-dependent effects such as a directional gravity wake and apply it to compact objects and cosmological scales. This work provides a rigorous foundation for further theoretical and experimental exploration of emergent gravity.