General Relativity & Quantum Cosmology

It is by now well established that black holes emit a thermal radiation and undergo an evaporation process. The original Hawking evaporation scenario, based on quantum fields on a classical background geometry, has been vastly extended and improved, in order to take into account in particular the backreaction of the radiation on the geometry. This can be done for example in a semiclassical setup, where the Einstein equations are sourced by an effective stress energy tensor. In two-dimensional models, this is a powerful method since the conformal anomaly enables one to reconstruct unambiguously the full effective stress energy tensor, or the corresponding effective matter action. However, attempts to generalize this method in four dimensions have been so far partly unsuccessful. In this talk we will review the difficulties that arise in attempts to constructing the effective action for matter fields coupled to a dilaton, and focus on a potential way out of the problem. This could lead to a new expression for the effective stress energy tensor on a black hole geometry, and to progress in the the study of backreaction in four-dimensional spherically symmetric models.