Numerical evolution of matter in dynamical axisymmetric black hole spacetimes - I. Methods and tests

We have developed a numerical code to study the evolution of self-gravitati ng matter in dynamic black hole axisymmetric spacetimes in general relativi ty. The matter fields are evolved with a high-resolution shock-capturing sc heme that uses the characteristic information of the general relativistic h ydrodynamic equations to build up a linearized Riemann solver. The spacetim e is evolved with an axisymmetric ADM code designed to evolve a wormhole in full general relativity. We discuss the numerical and algorithmic issues r elated 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 spacetimes. The code has been put through a series of tests that verify that it functions correctly. Particularly, we develop and descr ibe a new set of testbed calculations and techniques designed to handle dyn amically sliced, self-gravitating matter flows on black holes, and subject the code to these tests. We make some studies of the spherical and axisymme tric accretion onto a dynamic black hole, the fully dynamical evolution of imploding shells of dust with a black hole, the evolution of matter in rota ting spacetimes, the gravitational radiation induced by the presence of the matter fields and the behavior of apparent horizons through the evolution. (C) 2000 Elsevier Science B.V. All rights reserved.