Simple Gravity II: Field Equation and Spherical Solution

Key Points

• This work aims to introduce a nonlinear scalar field equation and derive its spherical solution within the Simple Gravity framework.
• Derivation of the nonlinear scalar field equation: ∇²Φ = 4πGρ + (1/c²)(∇Φ)².
• Analysis of spherical symmetry to obtain an exact solution.
• Comparison with the Newtonian limit to validate accuracy at large distances.
• The derived spherical solution recovers Newtonian gravity at large distances.
• Nonlinear effects are incorporated near massive bodies, enhancing accuracy in gravitational modeling.
• Establishes a field-theoretic foundation for the Simple Gravity theory.