Boundary conditions for AdS2 dilaton gravity

We study a bi-parametric family of dilaton gravity models with constant and negative curvature. This family includes the Jackiw-Teitelboim gravity and the Liouville gravity model induced by a bosonic string. Furthermore, this family is conformally equivalent to the hyperbolic dilaton models. We propose boundary conditions in the Fefferman-Graham and in the Eddington-Finkelstein gauge. We check the consistency of the asymptotic conditions by computing the entropy of their black hole solution.