ar X iv : h ep - t h / 93 02 13 2 v 1 2 6 Fe b 19 93 KANAZAWA - 93 - 01 Unrecognizable Black Holes in Two Dimensions

The classical 2D cosmological model of Callan, Giddings, Harvey and Strominger possesses a global symmetry that is responsible for decoupling of matter fields. The model is quantized on the basis of the extended phase space method to allow an exhaustive, algebraic analysis to find potential anomalies. Under a certain set of reasonable assumptions we show that neither the BRST symmetry of the theory nor the global symmetry suffers from an anomaly. From this we conclude that there is nothing to recognize the existence of black hole and therefore nothing to radiate in their cosmological model. (a) E-mail address: [email protected] (b) E-mail address: [email protected] (c) E-mail address: [email protected] 1 Inspired by string theory [1], much attention has recently paid to cosmology in twodimensions [2]. In particular, Callan, Giddings, Harvey and Strominger (CGHS) [3] have proposed a two-dimensional (2D) model in which the classically exact solutions to field equations correspond to black holes. Their model therefore has been considered as a theoretical laboratory to study the essence of black hole physics . The mass parameter in their black hole solution turns out to be arbitrary, and can not be related to the parameters of the theory. So, we are lead to wonder whether there is some sort of degeneracy. One of our findings in this letter is that in fact the global symmetry found in ref. [6] is responsible for “ degeneracy ” of the black hole back ground and at the same time for decoupling of the matter. To see this, we start by writing down the classical action of CGHS [3] S = ∫ dσ √ −g { exp(−2φ) [R(g) + 4 g∂αφ ∂βφ+ 4μ ] − 2 n