One can limit the range of length scales involved by introducing a viscosity, which is much larger than for a real astrophysical fluid, and one may also be forced to assume unrealistic values for some other parameters describing the fluid. Ultimately this means that rather than solving the problem with the desired parameters, one chooses parameters that can be handled by a modern supercomputer, and varies those parameters within the range that is allowed by the computer. The hope is that one will then be able to extrapolate from these simulations to the real world. The optical geometry is a particular conformal transformation that was proposed by members of our group and our collaborators. It fully agrees with Einstein's general relativity, but considerably simplifies the description of classical physics in strong, conformally static, gravitational fields.
Similar ideas are at the center of several approaches to quantum gravity.
We investigate applications of optical geometry to black hole electrodynamics, gravitational collapse, gravitational waves and cosmology. We have also in mind a possible application of optical geometry to a Hamiltonian formulation of gravity, compatible with some recent ideas of York and others. This could have a direct relevance for an optical geometry approach to quantum gravity.