Progress towards 3D black hole merger simulations

I review recent progress in 3D numerical relativity, focused on simulations involving black holes evolved with singularity avoiding slicings, but also touching on recent results in advanced techniques like black hole excision. After a long series of axisymmetric and perturbative studies of distorted black holes and black hole collisions, similar studies were carried out with full 3D codes. The results showed that such black hole simulations can be carried out extremely accurately, although instabilities plague the simulation at uncomfortably early times. However, new formulations of Einstein's equations allow much more stable 3D evolutions than ever before, enabling the first studies of 3D gravitational collapse to a black hole. With these new formulations, for example, it has been possible to perform the first detailed simulations of 3D grazing collisions of black holes with unequal mass, spin, and with orbital angular momentum. I discuss the 3D black hole physics that can now be studied, and prospects for the future, which look increasingly bright due to recent progress in formulations, black hole excision, new gauge conditions, and larger computers. Simulations may soon be able to provide information about the final plunge of two black holes, of relevance for gravitational wave astronomy. (author)