Quantum field theory in curved spacetime considers quantum fields propagating in a classical gravitational field. This approximation is useful to describe phenomena where the quantum nature of gravity does not play a crucial role and is therefore negligible. Quantum field theory in curved spacetimes is expected to break down when spacetime curvature approaches Planck scales and it needs to be replaced by a more general theory of quantum gravity. Nonetheless, within its range of validity it is possible to explore and study a wide range of phenomena which does not emerge in quantum field theory for inertial observers. Unruh effect, Hawking radiation and black holes thermodynamics are just some of the most famous examples.

At the moment, my Ph.D project includes two major research lines:

• the calculation, in spherical symmetric black hole spacetimes, of peculiar quantities such as the vacuum polarization and the fully regularized/renormalized stress-energy tensor (that combines classical contribution and quantum corrections), which is known to be plagued by divergencies;
• the analysis of quantum field theories with broken symmetries and the relative restoration, in generic spacetimes. In this case it is not even necessary for the spacetime to be curved. Simply considering two observers, whose reference frames are not related by a Lorentz transformation, is sufficient to observe non-trivial effect on the field theory.

The Ph.D project also leaves the door open to different lines of research, concerning quantum field theory in curved background or some aspect of quantum gravity, which will be better defined in the future.