Pulsar: repeatable Lagrangian singularity
  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. 
Alexander V. Chigirinsky