The classical 2D cosmological model of Callan, Giddings, Harvey and St
rominger possesses a global symmetry that is responsible for decouplin
g of matter fields. The model is quantized on the basis of the extende
d phase space method to allow an exhaustive, algebraic analysis to fin
d potential anomalies. Under a certain set of reasonable assumptions w
e show that neither the BRST symmetry of the theory nor the global sym
metry suffers from an anomaly. From this we conclude that there is not
hing to recognize the existence of a black hole and therefore nothing
to radiate in their cosmological model.