Thermal aspects in curved metrics

In this paper we describe two approaches that allow to calculate some thermal features as perceived by different observers in curved spacetimes: the tunnelling method and the Unruh-DeWitt detector. The tunnelling phenomenon is a semi-classical approach to the issue of Hawking radiation and allows a straightforward calculation of the horizon temperature in a plethora of scenarios; the Unruh-DeWitt model relies instead on a quantum field-theoretical approach and (whenever possible) gives a more exact answer in terms of transition rates between energy levels of an idealized detector.