  We consider a way to avoid black hole singularities by gluing a black hole
exterior to an interior with a tube-like geometry consisting of a direct
product of two-dimensional AdS, dS, or Rindler spacetime with a two-sphere of
constant radius. As a result we obtain a spacetime with either "cosmological"
or "acceleration" (event) horizons but without an apparent horizon. The inner
region is everywhere regular and supported by matter with the vacuum-like
equation of state $p_{r}+\rho =0$ where $p_{r}=T_{r}^{r}$ is the longitudinal
pressure, $\rho =-T_{0}^{0}$ is the energy density, $T_{\mu}^{\nu}$ is the
stress-energy tensor. When the surface of gluing approaches the horizon,
surface stresses vanish, while $p_{r}$ may acquire a finite jump on the
boundary. Such composite spacetimes accumulate an infinitely large amount of
matter inside the horizon but reveal themselves for an external observer as a
sphere of a finite ADM mass and size. If the throat of the inner region is
glued to two black hole exteriors, one obtains a wormhole of an arbitrarily
large length. Wormholes under discussion are static but not traversable, so the
null energy condition is not violated. In particular, they include the case
with an infinite proper distance to the throat. We construct also gravastars
with an infinite tube as a core and traversable wormholes connected by a finite
tube-like region.
