  In general, the interior of radially symmetric self-gravitating sphere is
considered in terms of hydrostatic equilibrium (HSE). This approach implies the
possibility of the static being of a body. Such a static state is assumed to be
the result of asymptotic damping of the process of formation. It is shown here
that the damping of this process is impossible: if a sphere vibrates radially,
then compressional wave is singular at the centre; dynamical singularity has no
intermediate stages of the fading; the HSE-state is unachievable.
Self-gravitating sphere perpetually vibrates in essentially singular way, it
contains dynamical central region -- pulsatile Lagrangian cavity. Theoretical
properties of this cavity indicate that this is a pulsar. A pulsar is common
structural feature for every self-gravitating structure.
