Stellar systems following the $R^{1/m}$ luminosity law. IV. The total
  energy and the central concentration of galaxies
  We expand our previous analytical and numerical studies of the family of
S\'ersic models, routinely used to describe early-type galaxies and the bulges
of spiral galaxies. In particular, we focus on the total energy budget, an
important dynamical property that has not been discussed in detail in previous
works. We use two different methods to calculate the total energy for the
S\'ersic model family, resulting in two independent expressions that can be
used along the entire sequence of S\'ersic models. We use these expressions to
investigate whether the Spitzer concentration index is a reliable measure for
the intrinsic 3D concentration of galaxies, and we conclude that it is not a
very useful measure for the central concentration. The popular Third Galaxy
Concentration index, on the other hand, is shown to be a reliable measure for
the intrinsic 3D concentration, even though it is based on the surface
brightness distribution and not on the intrinsic 3D density.
