On the dilaton gravity of analogue black holes

We investigate whether the gravity models realized by the typical two-dimensional analogue black holes of experimental platforms, such as superconducting quantum circuits, are indeed dilaton gravity models, and if so, how they can be classified. We identify the most reasonable assumptions these models must satisfy, and determine the dilaton models for which the state-dependence of the Hawking temperature, T, can be switched on and off, a feature that is absent in four dimensional black holes. When the analogue black hole exhibits state-independent temperature, as in the cases considered here, the kinematics governing T decouples from the dynamics underlying {the entropy} S. Our numerical analysis reveals that current experimental platforms yield a one-parameter family of unclassified dilaton potentials, which limits their usefulness for extracting theoretical insights. We then show that the logic can be easily inverted: starting from well-established dilaton models, one can derive the conditions that laboratory implementations must satisfy. This shifts the challenge from the theoretical perspective to the experimental realization.