Gralevity: A Tensor-Scalar Framework for Complementary Gravitational Dynamics and Energy Repulsion

Gralevity is introduced as a complementary theory to general relativity, retaining its predictive power while extending its scope. This framework posits that mass content of matter attracts other mass content (as described by standard gravity) while repelling the energy content of matter, mediated through a novel Repulsive Energy-Momentum Divergence Tensor (RμνR_{\mu\nu}Rμν). The introduction of a scalar field ϕ\phiϕ that interacts with the spacetime geometry forms the foundation of this interaction, offering a natural explanation for galactic rotation curves without dark matter, the accelerated expansion of the universe, and modifications to black hole physics. This paper presents the mathematical structure of Gralevity, analyzes specific scenarios of astrophysical and cosmological interest, and proposes observational tests to validate its predictions. Gralevity seeks to unify our understanding of gravitational phenomena while preserving compatibility with established principles of general relativity.