  In this letter, the open string is quantized in a time dependent black hole
background. The geometry is defined through an adiabatic approximation of the
Vaydia metric. The worldsheet two-point function is derived and it is shown to
have the same type of singularity as the flat space one. However, the equal
times two-point function depends on the particular Cauchy surface where the
worldsheet fields are defined. Finite temperature effects are incorporated
through the Liouville-von Neumann approach to non equilibrium thermodynamics.
