The most luminous events in the Universe are powered by accretion onto black holes. While nuclear burning releases less than a percent of rest mass energy accreting black holes can reach efficiencies around 40%.
Obviously general relativity plays an important role for such accretion
processes, in the most violent of them even the space-time geometry evolves
dynamically. For example, the accretion disks that are thought to power a
Gamma-Ray Burst require the solution of Einstein's equations of General Relativity.
I will present simulations of relativistic accretion disks, explain various
instabilities and discuss their possible observational implications.