Tackling conceptual problems in gravity with numerically simulated gedanken experiments

Gedanken experiments, also known as thought experiments, are an extremely powerful tool for studying conceptual problems in physics. The strategy is to devise fictitious experimental setups in which the effects one is interested in investigating clearly manifest, and can be better analyzed. In some cases it is necessary to predict the evolution of physical systems, a task that can become particularly hard when the theory is nonlinear. A possible approach to solve this issue is to perform a numerical integration of the evolution equations, thus simulating the gedanken experiment. In this thesis I will present three works, that I have carried out with different collaborators, in which such research technique has been used to tackle conceptual problems of different nature. In particular, in the first we performed extensive numerical simulations of the collapse of charged wave packets in Einstein-Maxwell and in Einstein-Maxwell-scalar theories of gravity, in the attempt of forming naked singularities and violate the weak cosmic censorship conjecture. In the second work we studied the fate of minimum mass black hole in Einstein-dilaton-Gauss-Bonnet gravity, when they undergo Hawking evaporation, by constructing a numerically simulated gedanken experiment in which we dynamically reduced the black hole mass by means of wave packets of a phantom field. Lastly, in the third work we simulated the nonlinear interaction between high-amplitude, low-frequency electromagnetic wave packets and a barrier of plasma, with the purpose of studying whether, in the scenario of the plasma-driven superradiant instability, the electromagnetic field can be confined in the vicinity of the black hole even during its exponential growth.