  It was known that an ideal spherically symmetric stellar system with
isotropic velocities and an inner core cannot reside in a Navarro, Frenk, and
White (NFW) gravitational potential. The incompatibility can be pinned down to
the radial gradient of the NFW potential in the very center of the system,
which differs from zero. The gradient is identically zero in an Einasto
potential, also an alternative representation of the dark matter (DM) halos
created by the kind of cold DM (CDM) defining the current cosmological model.
Here we show that, despite the inner gradient being zero, stellar cores are
also inconsistent with Einasto potentials. This result may have implications to
constrain the nature of DM through interpreting the stellar cores often
observed in dwarf galaxies.
