"The interaction of light with matter is traditionally studied in media that are either still or moving at a negligible fraction of the speed of light. In this regime standard text-book results apply. However, if the medium or, more generally speaking, certain parameters that distinguish the medium such as the refractive index are made to change or move close to the speed of light then new and unexpected scenarios emerge. For example, if the medium refractive index is not moving but is made to oscillate at high, e.g. optical frequencies, then a parametric interaction occurs with an incident light beam amplified transformed into a new pair of light beams. If closed within cavity mirrors, amplification by the oscillating medium is enhanced and even vacuum photons are be excited in correlated pairs in a process analogous to the dynamical Casimir effect. We will also consider the opposite regime in which the refractive index profile does not oscillate but is made to move forwards close to, or even faster than the speed of light. Again we encounter surprising effects: light propagating in such a moving medium finds an elegant description in terms of a space-time metric in which space is flowing in much the same way in which water flows in a river or in which space flows in a gravitational field. Under appropriate conditions the analogy can be extended to black holes and the analogue of an event horizon for light is formed by the perturbation. Light is frequency shifted at the horizon and is also amplified: the horizon acts as a parametric amplifier. The perturbations required for these and other related effects described in the proposal will be experimentally obtained using intense laser pulses and nonlinear optics and thus open a fascinating new area of laser physics."