The Nobel-Prize-winning detection of gravitational waves from binary black hole systems in 2015 by the Laser Interferometer Gravitational-Wave Observatory (LIGO) and the LIGO Scientific Collaboration has opened a new window on the universe. In addition, the 2017 observation of both gravitational and electromagnetic waves emitted by a binary neutron star system marked a new era of multi-messenger astronomy. While these successes are a remarkable experimental feat, they also constitute a significant computational achievement due to the crucial role played by accurate numerical models of the astrophysical sources in gravitational-wave data analysis. As current detectors are upgraded and new detectors come online within an international network of observatories, accurate, efficient, and advanced computational methods will be indispensable for interpreting the diversity of gravitational wave signals.

This Research Topic will focus on the fundamental mathematical and computational challenges in computational relativity and gravitational-wave data science. The aim of this special issue is to publish together the research efforts of pure and applied mathematicians, physicists, and statisticians with the goals of presenting the results of collaborations between these communities, working towards solving the most pressing mathematical modeling and numerical simulation issues facing the gravitational wave community, and focusing on important, pressing issues related to gravitational waves as well as providing mathematicians with new questions and problems to explore.

The Research Topic's areas of focus will be:

(i) mathematical and computational approaches for solving the source-free Einstein field equations (a nonlinear, coupled, hyperbolic-elliptic PDE system) including fundamental aspects of general relativity or alternative theories of gravity,

(ii) mathematical and computational approaches for the Einstein field equations with matter and magnetic fields, as well as the multi-scale, multi-physics modeling challenges for such problems,

(iii) methods for the detection, classification, and Bayesian inference of relativistic objects and gravitational-wave datasets, especially by considering under-explored techniques such as machine learning or uncertainty quantification.

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Frontiers in Applied Mathematics and Statistics

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