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

impose a boundary to the spacetime on the curve where e−2φchanges its sign(from a four-dimensional point of view the line e−2φ=0corresponds to the origin of the radial

coordinate r).This fact prevents the possibility of performing a change of coordinates to put the Rindler metric in a Minkowski form.But it is well-known that to Rindler coordinates is associated a constantflux of Hawking radiation,which is in this case of purely topological origin,and whose value turns out to coincide with the one calculated from(1).This mechanism is very similar to that discussed in[4]for two-dimensional anti-de Sitter spacetime,in the context of the Jackiw-Teitelboim model.

From our discussion will also emerge that the CGHS vacuum is semiclassically un-stable,unless one imposes a priori a cosmic censorship hypothesis(which can however be justified from a four-dimensional point of view).In doing that,we clarify some results obtained in[5]by means of a moving mirror model.Our arguments will also permit us to consistently define a mass for the dilaton Rindler spacetimes,which coincides with that of the conformally related CGHS solution.

Thefield equations stemming from(3)are:

R=0,∇2f i=0,

(gµν∇2−∇µ∇ν)e−2φ=2λ2+T(f)µν,(4) where T(f)

µνis the energy-momentum tensor for thefields f i.The general static solutions of these equations in the Schwarzschild gauge are given,for vanishing f i,by a locallyflat metric and a non-trivial dilaton,namely:

ds2=−(2λr−c)dt2+(2λr−c)−1dr2,

(5)

e−2φ=2λr+d.

Without loss of generality,one can take d=0.It is important to notice that the

static solutions arise naturally in Rindler coordinates[6].A change of coordinatesσ=√2λr−c sinhλt brings the metric to the Minkowski form λ−1

ds2=−dτ2+dσ2,but the dilaton becomes time-dependent,e−2φ=c+λ2(σ2−τ2).

The central point of this paper is however the observation that,if one wishes to have a real dilaton,one is forced to cut the spacetime at the curve where e−2φchanges its sign (r=0in the coordinates(5)),so that one cannot obtain the full Minkowski space even by changing coordinates.One can interpret the curve where e−2φvanishes as a singularity of spacetime.Indeed this curve corresponds to a true curvature singularity in the CGHS model,as one can easily verify performing the rescaling(2).For c>0,this singularity is shielded by a horizon at r=c/2λand is spacelike,while for c≤0it is naked and timelike. In the case c=0it coincides with the coordinate singularity and is lightlike.

It is also possible to assign a mass to the solutions(5)by means of the ADM procedure. In fact,one can define a conserved mass function[7]:

1

M=