Spacetime Discretization Methods for Numerical Relativity

Conventional approaches to numerical relativity (NR) rely on a 3+1 decomposition of spacetime that requires choosing a particular gauge which fixes the foliation of the spacetime. While the 3+1 approach has been known to work very well, e.g., for computing gravitational waveforms, it is not well-suited for a study of the strong field region near singularities. We investigate a different approach towards discretizing spacetime using spacetime volume elements that do not require an a priori choice of the foliation and are easier to adapt to complex geometries, e.g., in a binary black hole merger. We also explore spacetime elements with null or space-like boundaries that lead to a significant reduction in the communication overhead in parallel calculations, compared to conventional 3+1 NR codes which—due to the presence of time-like boundaries between grid components—require nearest-neighbour communication at every time step.