Conformal spacetime for the Einstein-Gauss-Bonnet theory in three dimensions

We consider the Einstein-Gauss-Bonnet theory in three dimensions and show that the continuum limit of the theory contains a form of a subleading black hole. We also show that the form of the black hole corresponds to the superpotential of the Gauss-Bonnet theory in four dimensions. We conclude that the form of the black hole in four dimensions corresponds to the one of the Gauss-Bonnet theory in three dimensions.