From Horndeski action to the Callan-Giddings-Harvey-Strominger model and beyond

The knowledge of what entered black hole (BH) is completely lost as it evaporates. This contradicts the unitarity principle of quantum mechanics and is referred to as the information loss paradox. Understanding the end stages of BH evaporation is key to resolving this paradox. As a first step, we need to have exact models that can mimic 4-D BHs in General relativity in classical limit and have a systematic way to include high-energy corrections. While there are various models in the literature, there is no systematic procedure by which one can study high-energy corrections. In this work, for the first time, we obtain Callan, Giddings, Harvey, and Strominger (CGHS) -- a (1+1)-D -- model from 4-D Horndeski action -- the most general scalar-tensor theory that does not lead to Ostrogradsky ghosts. We then show that 4-D Horndeski action can systematically provide a route to include higher-derivative terms relevant at the end stages of black hole evaporation. We derive the leading order Hawking flux while discussing some intriguing characteristics of the corrected CGHS models. We compare our results with other works and discuss the implications for primordial BHs.