Tunnelling methods and Unruh-DeWitt detectors in curved spacetimes

In this contribution we describe some interesting interplay between quantum theory, general relativity and thermodynamics. In order to highlight the connection between these theories, we describe two approaches that allow to calculate thermal features as perceived by different observers in curved spacetimes: the tunnelling method and the Unruh-DeWitt detector. In this context, the semi-classical tunnelling approach is applied to the issue of Hawking radiation and allows the calculation of the horizon temperature in a wide variety of scenarios. The Unruh-DeWitt model is instead a quantum field-theoretical approach that should give a more exact answer in terms of transition rates between energy levels of an idealized detector.