On the conformal equivalence between 2D black holes and Rind(5)

We study a two-dimensional dilaton gravity model related by a conformal transformation of the metric to the Callan-Giddings-Harvey-Strominger model. We find that most of the features and problems of the latter can be simply understood in terms of the class

thermal spectrum.Even though this radiation cannot be interpreted in the usual way as the Hawking radiation seen by an observer in an asymptoticallyflat region,its existence sheds some light on the properties of the CGHS model and is crucial to understand the physical equivalence of the models related by the rescaling(2).

Let us assume that the black hole is formed by the collapse of a f-wave.For example one can easily construct,using light-cone coordinates,solutions describing the collapse of a f-shock wave at y+=y+0:for y+≤y+0the solution is given by the vacuum solution (c=M=0),whereas for y+≥y+0a black hole is formed.The key point is that for the

vacuum solution the boundary at r=0is lightlike so that one can introduce coordinates

1

x±=±

e2πω/λ−1.(11) This is precisely the Planck spectrum for radiation at temperature given by(6).When integrated it gives the totalflux of f-particle energy:

λ2

G=