  Path equations of different orbiting objects in the presence of very strong
gravitational fields are essential to examine the impact of its gravitational
effect on the stability of each system. Implementing an analogous method, used
to examine the stability of planetary systems by solving the geodesic deviation
equations to obtain a finite value of the magnitude of its corresponding
deviation vectors. Thus, in order to know whether a system is stable or not,
the solution of corresponding deviation equations may give an indication about
the status of the stability for orbiting systems.Accordingly, two questions
must be addressed based on the status of stability of stellar objects orbiting
super-massive black holes in the galactic center.
  1. Would the deviation equations play the same relevant role of orbiting
planetary systems for massive spinning objects such as neutron stars or black
holes? 2. What type of field theory which describes such a strong gravitational
field ?
