  Hawking particles emitted by a black hole are usually found to have thermal
spectra, if not exactly, then by a very good approximation. Here, we argue
differently. It was discovered that spherical partial waves of in-going and
out-going matter can be described by unitary evolution operators independently,
which allows for studies of space-time properties that were not possible
before. Unitarity dictates space-time, as seen by a distant observer, to be
topologically non-trivial. Consequently, Hawking particles are only locally
thermal, but globally not: we explain why Hawking particles emerging from one
hemisphere of a black hole must be 100 % entangled with the Hawking particles
emerging from the other hemisphere. This produces exclusively pure quantum
states evolving in a unitary manner, and removes the interior region for the
outside observer, while it still completely agrees locally with the laws of
general relativity. Unitarity is a starting point; no other assumptions are
made. Region I and the diametrically opposite region II of the Penrose diagram
represent antipodal points in a PT or CPT relation, as was suggested before. On
the horizon itself, antipodal points are identified. A candidate instanton is
proposed to describe the formation and evaporation of virtual black holes of
the type described here. Some important explanations and discussion points are
added. In the latest of the paper, again some minor inaccuracies are corrected.
