A Saturation-Limited Vector–Tensor Theory of Gravitation

Key Points

• The aim is to develop a covariant theory of gravitation that incorporates a saturation constraint on a vector field.
• Introduced a covariant saturation-limited vector-tensor framework.
• Coupled the evolution of a metric tensor with a constrained timelike vector field.
• Formulated field equations that include a Lagrange multiplier for constraint enforcement.
• Recovered the exact Schwarzschild exterior solution using the theory.
• Admitted regular interior solutions with finite curvature invariants.
• Showed that the theory aligns with General Relativity under vacuum conditions and weak fields while introducing new properties.

Abstract