Resolving the Origins of Attractive and Repulsive Gravity via Symmetric and Antisymmetric Clifford Structures in Modified General Relativity
Abstract
Jau Tang
We present a unified algebraic framework that reconstructs both attractive and repulsive gravitational dynamics from the symmetric and antisymmetric sectors of the Clifford algebra Cl1,3. Building on prior work embedding Einstein’s field equations within symmetrized gamma matrix products, we show that attractive gravity naturally emerges from the symmetric bilinear space, which generates the metric and curvature tensors. Extending this structure, we demonstrate that antisymmetric bivector elements—typically linked to spin and torsion-produce a repulsive stress-energy contribution, offering a dynamic, operator-based origin for the cosmological constant.
This dual-sector formulation bridges the longstanding divide between curvature-induced gravity and vacuum-driven cosmic acceleration, unifying them within a single algebraic system. The resulting modified field equations remain fully tensorial and consistent with General Relativity, while introducing a physically grounded mechanism for cosmic repulsion. Our approach reproduces Einstein’s equations from the symmetric sector and reveals a previously overlooked role for the antisymmetric sector—one that yields repulsive gravity without invoking additional fields or arbitrary constants. These results suggest a new algebraic path toward unifying spacetime geometry with quantum field structure.
