Einstein-Grossmann geometry for frequency shifts of retrograde and direct orbits

TL;DR

The paper addresses the inadequacy of Newtonian gravity to explain frequency shifts between direct and retrograde orbits in rotating mass distributions. It adopts Einstein-Grossmann geodesics in a four-potential metric to derive exact mid-plane solutions and to analyze velocity differences for direct and retrograde circulations. The results show Zeeman-like shifts in orbital frequencies arising from metric gyro-potentials, with inner regions dominated by these effects and far regions approaching Keplerian behavior, all captured by roots $v_\pm = c\,\beta_\pm$ of a governing quadratic. These findings suggest testable deviations from Newtonian dynamics in the near zones of planets, disks, and galaxies, offering a geometric probe of spacetime structure via orbital dynamics.

Abstract

The metric gyro-potential of rotating distributions creates centripetal forces that can override Newtonian attraction on the inner and near-zone orbits. Einstein's geodesics in four metric potentials predict Zeeman-like shifts of Keplerian frequencies and measurable differences in the orbital speeds of direct and retrograde circulations.