[ExI] Gravity wave math

[Keith Henson]

If you want someone serious to chew on:

http://www.ams.org/journals/bull/2016-53-04/S0273-0979-2016-01544-8/

"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

Full-text PDF Free Access

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.

^^^^^^^^

The PDF is 42 pages.  It's not an easy read, but I think well worth it.

Keith

(Sorry for the duplicate post it has already been posted on the list.)