We study two dimensional dilaton gravity and supergravity following
hamiltonian methods. Firstly, we consider the structure of constraints of 2D
dilaton gravity and then the 2D dilaton supergravity is obtained taking the
squere root of the bosonic constraints. We integrate exactly the equations of
motion in both cases and we show that the solutions of the equation of motion
of 2D dilaton supergravity differs from the solutions of 2D dilaton gravity
only by boundary conditions on the fermionic variables, i.e. the black holes of
2D dilaton supergravity theory are exactly the same black holes of 2D bosonic
dilaton gravity modulo supersymmetry transformations. This result is the
bidimensional analogue of the no-hair theorem for supergravity.Comment: Plain Tex, 19pp, IPNO-TH 93/2
