  We explore self-similar hydrodynamic evolution of central voids embedded in
an isothermal gas of spherical symmetry under the self-gravity. More
specifically, we study voids expanding at constant radial speeds in an
isothermal gas and construct all types of possible void solutions without or
with shocks in surrounding envelopes. We examine properties of void boundaries
and outer envelopes. Voids without shocks are all bounded by overdense shells
and either inflows or outflows in the outer envelope may occur. These
solutions, referred to as type $\mathcal{X}$ void solutions, are further
divided into subtypes $\mathcal{X}_{\rm I}$ and $\mathcal{X}_{\rm II}$
according to their characteristic behaviours across the sonic critical line
(SCL). Void solutions with shocks in envelopes are referred to as type
$\mathcal{Z}$ voids and can have both dense and quasi-smooth edges.
Asymptotically, outflows, breezes, inflows, accretions and static outer
envelopes may all surround such type $\mathcal{Z}$ voids. Both cases of
constant and varying temperatures across isothermal shock fronts are analyzed;
they are referred to as types $\mathcal{Z}_{\rm I}$ and $\mathcal{Z}_{\rm II}$
void shock solutions. We apply the `phase net matching procedure' to construct
various self-similar void solutions. We also present analysis on void
generation mechanisms and describe several astrophysical applications. By
including self-gravity, gas pressure and shocks, our isothermal self-similar
void (ISSV) model is adaptable to various astrophysical systems such as
planetary nebulae, hot bubbles and superbubbles in the interstellar medium as
well as supernova remnants.
