  We consider the familiar junction conditions described by Israel for thin
timelike walls in Einstein-Hilbert gravity. One such condition requires the
induced metric to be continuous across the wall. Now, there are many spacetimes
with sources confined to a thin wall for which this condition is violated and
the Israel formalism does not apply. However, we explore the conjecture that
the induced metric is in fact continuous for any thin wall which models
spacetimes containing only positive energy matter. Thus, the usual junction
conditions would hold for all positive energy spacetimes. This conjecture is
proven in various special cases, including the case of static spacetimes with
spherical or planar symmetry as well as settings without symmetry which may be
sufficiently well approximated by smooth spacetimes with well-behaved null
geodesic congruences.
