Numerical evolution of matter in dynamical axisymmetric black hole spacetimes

We have developed a numerical code to study the evolution of self-gravitating matter in dynamic black hole axisymmetric spacetimes in general relativity. The matter fields are evolved with a high-resolution shock-capturing scheme that uses the characteristic information of the general relativistic hydrodynamic equations to build up a linearized Riemann solver. The spacetime is evolved with an axisymmetric ADM code designed to evolve a wormhole in full general relativity. We discuss the numerical and algorithmic issues related to the effective coupling of the hydrodynamical and spacetime pieces of the code, as well as the numerical methods and gauge conditions we use to evolve such spacetime…