  With proper physical mechanisms of energy and momentum input from around the
centre of a self-gravitating polytropic gas sphere, a central spherical "void"
or "cavity" or "bubble" of very much less mass contents may emerge and then
dynamically expand into a variety of surrounding more massive gas envelopes
with or without shocks. We explore self-similar evolution of a self-gravitating
polytropic hydrodynamic flow of spherical symmetry with such an expanding
"void" embedded around the center. The void boundary supporting a massive
envelope represents a pressure-balanced contact discontinuity where drastic
changes in mass density and temperature occur. We obtain numerical void
solutions that can cross the sonic critical surface either smoothly or by
shocks. Using the conventional polytropic equation of state, we construct
global void solutions with shocks travelling into various envelopes including
static polytropic sphere, outflow, inflow, breeze and contraction types. In the
context of supernovae, we discuss the possible scenario of separating a central
collapsing compact object from an outgoing gas envelope with a powerful void in
dynamic expansion. Initially, a central bubble is carved out by an extremely
powerful neutrinosphere. After the escape of neutrinos during the decoupling,
the strong electromagnetic radiation field and/or electron-positron pair plasma
continue to drive the cavity expansion. In a self-similar dynamic evolution,
the pressure across the contact discontinuity decreases with time to a
negligible level for a sufficiently long lapse and eventually, the gas envelope
continues to expand by inertia. We describe model cases of polytropic index
$\gamma=4/3-\epsilon$ with $\epsilon>0$ and discuss pertinent requirements to
justify our proposed scenario.
