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The recent observations.
:<math> \bar{h}_{ij} =</math> gravitational wave, and <math>I_{ij} =</math> mass quadrupole moment.
:<math> \bar{h}_{ij} =</math> gravitational wave, and <math>I_{ij} =</math> mass quadrupole moment.
The results of his findings were published in 1916 as ''Näherungsweise Integration der Feldgleichungen der Gravitation'' (''"Approximate Integration of the Field Equations of Gravitation"''),<ref>Einstein, Albert. "Näherungsweise Integration der Feldgleichungen der Gravitation"; ''Proceedings of the Royal Prussian Academy of Sciences'' (1916), Berlin, Germany.</ref> but serious errors led him to a revision, published in 1918 as ''Über Gravitationswellen'' (''"About Gravitational Waves"'')<ref>Einstein, Albert. "Über Gravitationswellen"; ''Proceedings of the Royal Prussian Academy of Sciences'' (1918), Berlin, Germany.
The results of his findings were published in 1916 as ''Näherungsweise Integration der Feldgleichungen der Gravitation'' (''"Approximate Integration of the Field Equations of Gravitation"''),<ref>Einstein, Albert. "Näherungsweise Integration der Feldgleichungen der Gravitation"; ''Proceedings of the Royal Prussian Academy of Sciences'' (1916), Berlin, Germany.</ref> but serious errors led him to a revision, published in 1918 as ''Über Gravitationswellen'' (''"About Gravitational Waves"'')<ref>Einstein, Albert. "Über Gravitationswellen"; ''Proceedings of the Royal Prussian Academy of Sciences'' (1918), Berlin, Germany.</ref>.
</ref>.
== The LIGO observations of 2015 ==
Because gravitational waves from distant (billions of light years away) phenomena are incredibly faint, detecting them has been a daunting task. Decades of work have gone into the development of sufficiently sensitive detectors. In 2015, the [[LIGO]] detectors (one in Hanford, Washington and one in Livingston Louisiana) made the first detection of the waves.
=== The event of September 14, 2015 ===
This event was observed shortly after turning on the enhanced version of the LIGO detection system, and reported in January 2016.<ref>http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.116.061102]</ref> Making sure that it wasn't a detection of random noise required comparing the waveforms with the predicted waveforms from theoretical calculations of the final approach and "ringdown" of a merger of two black holes. The signal closely matched theoretical predictions.<ref>https://www.ligo.caltech.edu/image/ligo20160211a</ref>
The match showed a confidence of better than "five sigma", that is, a probability of less than one in a million that this was a coincidence. The same event was detected at both observatories, a small fraction of a second apart, as the wave passed through the Earth.
Unlike most astronomical wave phenomena, the gravitational waves from black hole mergers are approximately in the audible range. With only a small amount of signal processing, the signal was made audible; it's sort of a "chirp".<ref>https://www.ligo.caltech.edu/video/ligo20160211v2</ref> For a while this "chirp" became something of an internet sensation.
Other articles: [http://www.nbcnews.com/science/science-news/gravitational-waves-ripples-space-time-detected-first-time-n516566], [https://www.youtube.com/watch?v=aEPIwEJmZyE]
=== The event of December 26, 2015 ===
A second black hole merger was detected two months later.<ref>http://www.nbcnews.com/science/science-news/it-wasn-t-fluke-scientists-see-black-holes-collide-again-n593156</ref><ref>http://www.cbsnews.com/news/scientists-detect-second-gravitational-wave-einstein-predicted/</ref><ref>https://www.ligo.caltech.edu/news/ligo20160615</ref>
Here is a comparison of the "chirps" from the two events. The December event was significantly less powerful that the September one<ref>https://www.ligo.caltech.edu/video/ligo20160615v2</ref>
== The LISA project ==
An even more ambitious and sensitive detector, previously called LISA and now called eLISA (Evolved Laser Interferometer Space Antenna), is being designed by an international consortium of agencies. This one involves satellites in heliocentric orbit, using laser interferometers to measure changes in the distance between "test masses" inside the satellites.
A test of the underlying test mass technology, called the LISA Pathfinder test, succeeded on June 6, 2016.<ref>http://www.bbc.co.uk/news/science-environment-36472434#sa-ns_mchannel=rss&ns_source=PublicRSS20-sa</ref>
== See also ==
== See also ==