Quantum field theory in curved spacetime provides a powerful framework to study quantum effects in cosmology and black hole physics. Unlike in flat spacetime QFT, curvature requires renormalization already at the level of the free theory. This yields a renormalized stress-energy tensor for quantum fields on a given background, capturing effects such as Hawking radiation of black holes and particle production in expanding universes. The next step is to include the effect of quantum fields on spacetime geometry, the so-called backreaction problem.
In this seminar, I introduce this framework, highlight its main challenges, and present effective two-dimensional black hole models that address them while retaining the essential quantum features. In two dimensions, the renormalized stress-energy tensor can be written in closed form in terms of the metric, transforming the semiclassical equations into a second-order system of PDEs. This makes it possible to study the full dynamics, including backreaction.