Sedimentation equilibrium of globular and galaxy clusters

The equilibrium of globular and galaxy clusters is analyzed using a gravitomagnetic (GM) model for a fluid in stationary, axially-symmetric motion. An oblique change of coordinates leads to a free-fall nonlinear force balance equation relating the GM flux function and the gravitational potential. An approximate internal solution of the force balance is obtained introducing trial functions in the form of a sedimentation equilibrium. The internal solution defines the tangential component of the GM field acting on the surface of the cluster. This GM component constitutes the boundary condition that must be used to obtain a self-consistent solution together with Gauss' and Ampere's laws. The complete solution is postponed for future work, but a simple application to the classic Coma Cluster problem indicates that the rotating velocity on the surface of the cluster is within the range of observed values, without introducing dark matter.