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 for and analysis of detected signals. 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.
When writing the conclusion part of your abstract, remember that these conclusions should be precise and concise. There is no need to re-summarise what you have already discussed or the contents of your dissertation. This is an informative abstract, not a descriptive one. If you are unsure of the difference, you may find the section, Choosing between dissertation abstract styles: Descriptive and informative , helpful. Furthermore, be careful not to make claims that cannot be supported by your findings. There is always a danger to over-exaggerate and/or over-generalise in this part of the abstract, which should be avoided. It is unlikely that you will have changed the world through your study, but you may still have added something significant to the literature, so try and strike the right balance.