| The problem of detecting gravitational radiation is receiving considerable attention with the construction of new detectors in the United States, Europe and Japan. The theoretical modeling of the wave forms that would be produced in particular systems will expedite the search and analysis of the detected signals. Furthermore, these models will also help to shed light on our understanding of these sources.; The most promising candidates to produce gravitational radiation of detectable amplitude are systems containing black holes or neutron stars. The strong-field associated with these systems allow us ignore the influence of distant matter and study the problem as if the source were isolated. Although this assumption simplifies the treatment of the problem, because of the structure of Einstein's equations, an analytical study is almost impossible. Also, perturbative analysis will be grossly inaccurate because of the strong fields present near the source. Hence, numerical techniques must be employed for a correct description of the system. In this work, a numerical implementation of Einstein's equations is presented in a characteristic formulation, which is particularly useful to study the propagation of gravitational wave forms through spacetime.; The characteristic formulation of GR is implemented to obtain an algorithm capable of evolving black holes in 3D asymptotically flat spacetimes. Using compactification techniques, future null infinity is included in the evolved region, which enables the unambiguous calculation of the radiation produced by some compact source. A module to calculate the waveforms is constructed and included in the evolution algorithm. This code is shown to be second-order convergent and to handle highly non-linear spacetimes. In particular, we have shown that the code can handle spacetimes whose radiation is equivalent to a galaxy converting its whole mass into gravitational radiation in one second.; We further use the characteristic formulation to treat the region close to the singularity in black hole spacetimes. The code carefully excises a region surrounding the singularity and accurately evolves generic black hole spacetimes with apparently unlimited stability. |
