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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



The emergence of gravitational wave science: 100 years of development of mathematical theory, detectors, numerical algorithms, and data analysis tools

Authors: Michael Holst, Olivier Sarbach, Manuel Tiglio and Michele Vallisneri
Journal: Bull. Amer. Math. Soc. 53 (2016), 513-554
MSC (2010): Primary 83-XX, 35-XX, 65-XX; Secondary 53-XX, 68-XX, 85-XX
Published electronically: August 2, 2016
MathSciNet review: 3544260
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Abstract: 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.

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Additional Information

Michael Holst
Affiliation: Department of Mathematics, Department of Physics, University of California San Diego, La Jolla California 92093 – and – Center for Computational Mathematics, Center for Astrophysics and Space Sciences, University of California San Diego, La Jolla California 92093

Olivier Sarbach
Affiliation: Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Ciudad Universitaria, 58040 Morelia, Michoacán, México

Manuel Tiglio
Affiliation: Center for Computational Mathematics, Center for Astrophysics and Space Sciences, University of California San Diego, La Jolla California 92093 – and – San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093

Michele Vallisneri
Affiliation: Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California 91109 – and – TAPIR Group, MC 350-17, California Institute of Technology, Pasadena, California 91125

Received by editor(s): May 23, 2016
Published electronically: August 2, 2016
Dedicated: In memory of Sergio Dain
Article copyright: © Copyright 2016 American Mathematical Society

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