  We have obtained a criterion for spherically symmetric and static structures
under hydrostatic equilibrium in general relativity (GR), which states that for
a given value of $\sigma \equiv (P_0/E_0) \equiv $ the ratio of central
pressure to central energy-density], the compaction parameter $u \equiv (M/a)$,
where $M$ is the total mass and $a$ is the radius of the configuration] or the
surface redshift of any regular configuration cannot exceed that of the
corresponding homogeneous density sphere, that is, $u \leq u_h$, where $u_h$ is
the compaction parameter of the homogeneous density sphere. By examining
various exact solutions and surface). On the other hand, configurations having
a finite density on the surface (that is, the self-bound structures) do not
fulfill this criterion. This criterion puts a severe restriction on the static
structures based upon the general relativistic field equations and consequently
on the upper limit of mass, surface and central redshift and other physical
parameters of spherically symmetric and static configurations.
