  String theory in Euclidean flat space with a spacelike linear dilaton
contains a D1-brane which looks like a semi-infinite hairpin. In addition to
its curved shape, this ``hairpin brane'' has a condensate of the open string
tachyon stretched between its two sides. The tachyon smears the brane and
shifts the location of its tip. The Minkowski continuation of the hairpin brane
describes a D0-brane freely falling in a linear dilaton background. Effects
that in Euclidean space are attributed to the tachyon condensate, give rise in
the Minkowski case to a stringy smearing of the trajectory of the D-brane by an
amount that grows as its acceleration increases. When the Unruh temperature of
the brane reaches the Hagedorn temperature of perturbative string theory in the
throat, the rolling D-brane state becomes non-normalizable. We propose that
black holes in string theory exhibit similar properties. The Euclidean black
hole solution has a condensate of a tachyon winding around Euclidean time. The
Minkowski manifestation of this condensate is a smearing of the geometry in a
layer around the horizon. As the Hawking temperature, T_{bh}, increases, the
width of this layer grows. When T_{bh} reaches the Hagedorn temperature, the
size of this ``smeared horizon'' diverges, and the black hole becomes
non-normalizable. This provides a new point of view on the string/black hole
transition.
