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A general dilaton gravity theory in 1+1 spacetime dimensions, with a cosmological constant and a new dimensionless parameter, contains as special cases the constant curvature theory of Teitelboim and Jackiw, the theory equivalent to vacuum planar general relativity, the first-order string theory, and a two-dimensional purely geometrical theory. The equations of this general two-dimensional theory admit several different black holes with various types of singularities. The singularities can be spacelike, timelike, or null, and there are even cases without singularities. Evaluation of the ADM mass, as a charge density integral, is possible in some situations by carefully subtracting the black hole solution from the corresponding linear dilation at infinity.
Lemos et al. (Tue,) studied this question.