  We discuss a new class of solutions to the Einstein equations which describe
a primordial black hole (PBH) in a flat Friedmann background. Such solutions
arise if a Schwarzschild black hole is patched onto a Friedmann background via
a transition region. They are possible providing the black hole event horizon
is larger than the cosmological apparent horizon. Such solutions have a number
of strange features. In particular, one has to define the black hole and
cosmological horizons carefully and one then finds that the mass contained
within the black hole event horizon decreases when it is larger than the
Friedmann cosmological apparent horizon, although its area always increases.
These solutions involve two distinct future null infinities and are interpreted
as the conversion of a white hole into a black hole. Although such solutions
may not form from gravitational collapse in the same way as standard PBHs,
there is nothing unphysical about them, since all energy and causality
conditions are satisfied. Their conformal diagram is a natural amalgamation of
the Kruskal diagram for the extended Schwarzschild solution and the conformal
diagram for a black hole in a flat Friedmann background. In this paper, such
solutions are obtained numerically for a spherically symmetric universe
containing a massless scalar field, but it is likely that they exist for more
general matter fields and less symmetric systems.
