  The non-rotating BTZ solution is expressed in terms of coordinates that allow
for an arbitrary time-dependent scale factor in the boundary metric. We provide
explicit expressions for the coordinate transformation that generates this form
of the metric, and determine the regions of the complete Penrose diagram that
are convered by our parametrization. This construction is utilized in order to
compute the stress-energy tensor of the dual CFT on a time-dependent
background. We study in detail the expansion of radial null geodesic
congruences in the BTZ background for various forms of the scale factor of the
boundary metric. We also discuss the relevance of our construction for the
holographic calculation of the entanglement entropy of the dual CFT on
time-dependent backgrounds.
