The emergence of gravitational wave science: 100 years of development of mathematical theory, detectors, numerical algorithms, and data analysis tools
On September 14, 2015, the newly upgraded Laser Interferometer Gravitational-wave Observatory (LIGO) recorded a loud gravitational-wave (GW) signal, emitted a billion light-years away by a coalescing binary of two stellar-mass black holes. The detection was announced in February 2016, in time for the hundredth anniversary of Einstein's prediction of GWs within the theory of general relativity (GR). The signal represents the first direct detection of GWs, the first observation of a black-hole binary, and the first test of GR in its strong-field, high-velocity, nonlinear regime. In the remainder of its first observing run, LIGO observed two more signals from black-hole binaries, one moderately loud, another at the boundary of statistical significance. The detections mark the end of a decades-long quest and the beginning of GW astronomy: finally, we are able to probe the unseen, electromagnetically dark Universe by listening to it. In this article, we present a short historical overview of GW science: this young discipline combines GR, arguably the crowning achievement of classical physics, with record-setting, ultra-low-noise laser interferometry, and with some of the most powerful developments in the theory of differential geometry, partial differential equations, high-performance computation, numerical analysis, signal processing, statistical inference, and data science. Our emphasis is on the synergy between these disciplines and how mathematics, broadly understood, has historically played, and continues to play, a crucial role in the development of GW science. We focus on black holes, which are very pure mathematical solutions of Einstein's gravitational-field equations that are nevertheless realized in Nature and that provided the first observed signals.
© 2016 American Mathematical Society. Article electronically published on August 2, 2016. We thank the reviewers as well as David Shoemaker, who read preliminary drafts, for their feedback and comments. This work was supported in part by NSF grants PHY-1500818, DMS/FRG-1262982, and DMS/CM-1217175 to the University of California at San Diego, by NSF grant PHY-1404569 to the California Institute of Technology, by CONACyT grant No. 271904, and by a CIC grant to Universidad Michoacana. Part of this research was performed at the Jet Propulsion Laboratory, under contract with the National Aeronautics and Space Administration.
Submitted - 1607.05251.pdf