The No-Hair Conjecture in 2D Dilaton Supergravity

TL;DR

This paper demonstrates that in 2D dilaton supergravity, black hole solutions are essentially the same as in bosonic dilaton gravity, differing only by boundary conditions on fermionic variables, thus extending the no-hair conjecture to supergravity.

Contribution

It shows that 2D dilaton supergravity solutions are identical to bosonic solutions up to boundary conditions, providing a supersymmetric extension of the no-hair theorem.

Findings

Black hole solutions in 2D dilaton supergravity match those in bosonic dilaton gravity.

Solutions differ only by boundary conditions on fermionic variables.

The results extend the no-hair theorem to 2D supergravity.

Abstract

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.