  It has been proposed that a certain Z_N orbifold, analytically continued in
N, can be used to describe the thermodynamics of Rindler space in string
theory. In this paper, we attempt to implement this idea for the open-string
sector. The most interesting result is that, although the orbifold is tachyonic
for positive integer N, the tachyon seems to disappear after analytic
continuation to the region that is appropriate for computing ${\mathrm {Tr}}
\rho^{\mathcal N}$, where $\rho$ is the density matrix of Rindler space and Re
$\mathcal N$>1. Analytic continuation of the full orbifold conformal field
theory remains a challenge, but we find some evidence that if such analytic
continuation is possible, the resulting theory is a logarithmic conformal field
theory, necessarily nonunitary.
