Superradiance in black hole spacetimes is a phenomenon by which a field of spin 0 or 1 can extract energy from the background. Typically, one can imagine sending a wave packet with a given energy towards a black hole and receiving in return a superposition of wave packets carrying a total amount of energy that is larger than the energy sent in. It can be caused by rotation or by interaction between the charges of the black hole and the field. In the first case, the region where superradiance takes place (the ergoregion) has a clear geometrical localization depending only on the physical parameters of the black hole. For charge induced superradiance, this is not the case and we have a generalized ergoregion depending also on the physical properties of the field (mass, charge, angular momentum). In the most severe cases, the generalized ergoregion may cover the whole exterior of the black hole. We focus on charge-induced superradiance for spin 0 fields in spherically symmetric situations. Alain Bachelot wrote a thorough theoretical study of this question in 2004, which, to my knowledge, is the only work of its kind. When I was in Bordeaux, he and I discussed the possibility of investigating superradiance numerically. Over the years it became an actual research project, involving Laurent Di Menza and more recently Mathieu Pellen, of which this talk is an account. The idea was to observe numerically some superradiant behaviours and gain a more precise understanding of the phenomenon. We shall show an exact analogue of the Penrose process with the superradiance of wave packets and a slightly different behaviour for fields "emerging" inside the ergoregion. We shall also explore the related question of black hole bombs and present some recent observations.
