| A new field of astrophysics is beginning to form. The advent of very large gravitational radiation detectors will soon make it possible to study the physics of distant catastrophic phenomena by the gravitational radiation that is emitted. However, before any physical interpretations can be extracted from the waveforms, there must be a way of associating particular features in the waveforms with types of events. This association can only be made after a catalog of synthetic waveforms is created. Mergers of binary black holes are one of the strongest theoretical sources of gravitational radiation. However, calculations of the complete waveforms produced during binary black hole mergers require sophisticated numerical codes that solve Einstein's equation in the non-linear regime. The accuracy of these numerical codes must be confirmed before any reliable waveform can be obtained. Ideally, these codes would be tested against a large set of known solutions. Unfortunately, few solutions are known and one must resort to less thorough tests. Here we present tests of the non-linear ‘Pitt Null Code’ based on perturbative calculations and Cauchy convergence.; We present a new method for calculating the late-time perturbative waveforms from binary black hole mergers. Our method consists of a two-stage characteristic evolution of the perturbative Teukolsky equations. Stage I involves calculating the waveform from a binary white hole fission, and stage II involves the conversion of this white hole waveform into a black hole waveform. Our tests confirm that the ‘Pitt Null Code’ can reproduce the stage I perturbative calculations to the expected second order accuracy. We have also found that the ‘Pitt Null Code’ is second order Cauchy convergent in the mildly non-linear regime.; We were able to discover several interesting features of this two-step technique: (i) the white hole waveforms show a strong dependence on the parameters that describe the energetics of the fission, (ii) the black hole waveforms show a mild dependence on these parameters, (iii) the black hole waveforms show a spurious ‘ring-up’, (iv) the black hole event horizon differs by more than a time-reflection from the original white hole horizon. |
