Gravitational waves carry information about their source, and their detection will uncover facets of our universe, otherwise invisible. Recently, we made publicly available a waveform computation tool, the PITT code, as part of the Einstein Toolkit open software for relativistic astrophysics. The code implements the “characteristic method,” which computes the gravitational waves infinitely far from their source in terms of compactified light cones. We proved that our code produces waveforms that satisfy the demands of next generation detectors. However, the main problem is that the well-posedness of the Einstein equations in characteristic formulation is not proven. Here we present our progress towards developing and testing a new computational evolution algorithm based on the well-posedness of the characteristic evolution. We analyze the well-posedness of the problem for quasi-linear scalar waves propagating on an asymptotically flat curved space background with source, in null Bondi-Sachs coordinates. We design a new numerical boundary and evolution algorithm, and proved that is stable both numerically and analytically. We built and run numerical tests to confirm the well-posedness and stability properties of the new algorithm. The knowledge gained from the model problems considered here should be of benefit to a better understanding of the gravitational case. A new characteristic code based upon well-posedness would be of great value.
Babiuc, M. & Winicour, J. (2013, July). Well-posedness of characteristic evolution in Bondi coordinates. Poster session presented at the 20th International Conference on General Relativity and Gravitation and10th Amaldi Conference on Gravitational Waves. Warsaw, Poland.