Author(s)

Richard James Petti¹, Jacob Luke Graham²

¹Arlington, MA, USA.
²Newton, MA, USA.

Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with differential geometry. This work extends General Relativity and Einstein-Cartan theory by augmenting the Poincaré group with projective (special) conformal transformations, which are translations at conformal infinity. Momentum becomes a part of the differential geometry of spacetime. The Lie algebra of these transformations is represented by vectorfields on an associated Minkowski fiber space. Variation of projective conformal scalar curvature generates a 2-index tensor that serves as linear momentum in the field equations of General Relativity. The computation yields a constructive realization of Mach’s principle: local inertia is determined by local motion relative to mass at conformal infinity in each fiber. The vectorfields have a cellular structure that is similar to that of turbulent fluids.

Projective Symmetry, Conformal Symmetry, Momentum, General Relativity, Einstein-Cartan Mach’s Principle

Petti, R. and Graham, J. (2024) Momentum as Translations at Conformal Infinity. Journal of Applied Mathematics and Physics, 12, 1522-1540. doi: 10.4236/jamp.2024.124093.