We consider the entanglement of closed bosonic strings intersecting the event
horizon of a Rindler spacetime and, by using some simplified (rather
semiclassical) arguments and some elements of the string field theory, we show
the existence of a critical temperature beyond which closed strings
\emph{cannot be in thermal equilibrium}. The order of magnitude of this
critical value coincides with the Hagedorn temperature, which suggests an
interpretation consistent with the fact of having a partition function which is
bad defined for temperatures higher than it. Possible implications of the
present approach on the microscopical structure of stretched horizons are also
pointed out.Comment: A detailed description of string boundary states in a Rindler horizon
was added, and their relation with the stretched horizon microscopic
structure was emphasized. References added. To appear in Eur. Phys. J.
