Abstract

We study two-dimensional (2D) dilaton gravity and supergravity following Hamiltonian methods. First, we consider the structure of constraints of 2D dilaton gravity, and then the 2D dilaton supergravity theory is obtained taking the square 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 differ 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 two-dimensional analogue of the no-hair theorem for supergravity.