A Geometric Momentum-Transfer Extension of General Relativity

This work develops a minimal geometric extension of General Relativity in which irreversible momentum transfer is encoded directly in the gravitational sector through a Weyl–Bach contribution. The matter sector remains unmodified and locally conserved, while spacetime geometry acquires an active feedback channel capable of absorbing and regulating momentum flow. Within this framework, redshift, time dilation, and the Tolman surface-brightness relation emerge from a single cumulative geometric mechanism acting along worldlines, without invoking metric expansion, evolving scale factors, or phenomenological attenuation. The Hubble parameter enters only as a calibration scale for long-time geometric drift, rather than as a dynamical expansion rate. Beyond light propagation, the same geometric mechanism provides curvature-dependent feedback in strong-field regimes, suggesting a natural pathway toward regulating classical singularities without exotic matter or violations of local conservation laws. The framework is formulated in a manner compatible with analytical investigation and numerical relativity implementations. This work is intended as a foundation for further mathematical analysis, physical validation, and collaborative development.