  We revisit non-interacting string partition functions in Rindler space by
summing over fields in the spectrum. In field theory, the total partition
function splits in a natural way in a piece that does not contain surface terms
and a piece consisting of solely the so-called edge states. For open strings,
we illustrate that surface contributions to the higher spin fields correspond
to open strings piercing the Rindler origin, unifying the higher spin surface
contributions in string language. For closed strings, we demonstrate that the
string partition function is not quite the same as the sum over the partition
functions of the fields in the spectrum: an infinite overcounting is present
for the latter. Next we study the partition functions obtained by excluding the
surface terms. Using recent results of JHEP 1505 (2015) 106, this construction,
first done by Emparan, can be put on much firmer ground. We generalize to type
II and heterotic superstrings and demonstrate modular invariance. All of these
exhibit an IR divergence that can be interpreted as a maximal acceleration
close to the black hole horizon. Ultimately, since these partition functions
are only part of the full story, divergences here should not be viewed as a
failure of string theory: maximal acceleration is a feature of a faulty
treatment of the higher spin fields in the string spectrum. We comment on the
relevance of this to Solodukhin's recent proposal. A possible link with the
firewall paradox is apparent.
