NO-HAIR CONJECTURE IN 2-DIMENSIONAL DILATON SUPERGRAVITY

We study two-dimensional (2D) dilaton gravity and supergravity followi ng Hamiltonian methods. First, we consider the structure of constraint s of 2D dilaton gravity, and then the 2D dilaton supergravity theory i s obtained taking the square root of the bosonic constraints. We integ rate exactly the equations of motion in both cases, and we show that t he solutions of the equation of motion of 2D dilaton supergravity diff er from the solutions of 2D dilaton gravity only by boundary condition s on the fermionic variables; i.e., the black holes of 2D dilaton supe rgravity 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.