Editing General relativity (section)

=== Gravitational waves ===
{{Main|Gravitational wave}}
[[File:Gravwav.gif|thumb|Ring of test particles deformed by a passing (linearized, amplified for better visibility) gravitational wave]]
Predicted in 1916<ref>{{cite journal|author=Einstein, A|title=Näherungsweise Integration der Feldgleichungen der Gravitation|date=22 June 1916|url=http://einstein-annalen.mpiwg-berlin.mpg.de/related_texts/sitzungsberichte|journal=[[Prussian Academy of Sciences|Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften Berlin]]|issue=part&nbsp;1|pages=688–696|bibcode=1916SPAW.......688E|access-date=12 February 2016|archive-url=https://web.archive.org/web/20190321062928/http://einstein-annalen.mpiwg-berlin.mpg.de/related_texts/sitzungsberichte|archive-date=21 March 2019}}</ref><ref>{{cite journal|author=Einstein, A|title=Über Gravitationswellen|date=31 January 1918|url=http://einstein-annalen.mpiwg-berlin.mpg.de/related_texts/sitzungsberichte|journal=Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften Berlin|issue=part&nbsp;1|pages=154–167|bibcode=1918SPAW.......154E|access-date=12 February 2016|archive-url=https://web.archive.org/web/20190321062928/http://einstein-annalen.mpiwg-berlin.mpg.de/related_texts/sitzungsberichte|archive-date=21 March 2019}}</ref> by Albert Einstein, there are gravitational waves: ripples in the metric of spacetime that propagate at the speed of light. These are one of several analogies between weak-field gravity and electromagnetism in that, they are analogous to [[electromagnetic wave]]s. On 11 February 2016, the Advanced LIGO team announced that they had [[Gravitational wave observation|directly detected gravitational waves]] from a [[Binary black hole|pair]] of black holes [[Stellar collision|merging]].<ref name="Discovery 2016">{{cite journal |title=Einstein's gravitational waves found at last |journal=Nature News| url=http://www.nature.com/news/einstein-s-gravitational-waves-found-at-last-1.19361 |date=11 February 2016 |last1= Castelvecchi |first1=Davide |last2=Witze |first2=Witze |doi=10.1038/nature.2016.19361 |s2cid=182916902|access-date= 11 February 2016 }}</ref><ref name="Abbot">{{cite journal |title=Observation of Gravitational Waves from a Binary Black Hole Merger| author1=B. P. Abbott |collaboration=LIGO Scientific Collaboration and Virgo Collaboration| journal=Physical Review Letters| year=2016| volume=116|issue=6| doi= 10.1103/PhysRevLett.116.061102 | pmid=26918975| page=061102|arxiv = 1602.03837 |bibcode = 2016PhRvL.116f1102A | s2cid=124959784 }}</ref><ref name="NSF">{{cite web|title = Gravitational waves detected 100 years after Einstein's prediction |website= NSF – National Science Foundation|url = https://www.nsf.gov/news/news_summ.jsp?cntn_id=137628 |date = 11 February 2016}}</ref>

The simplest type of such a wave can be visualized by its action on a ring of freely floating particles. A sine wave propagating through such a ring towards the reader distorts the ring in a characteristic, rhythmic fashion (animated image to the right).<ref>Most advanced textbooks on general relativity contain a description of these properties, e.g. {{Harvnb|Schutz|1985|loc=ch. 9}}</ref> Since Einstein's equations are [[non-linear]], arbitrarily strong gravitational waves do not obey [[linear superposition]], making their description difficult. However, linear approximations of gravitational waves are sufficiently accurate to describe the exceedingly weak waves that are expected to arrive here on Earth from far-off cosmic events, which typically result in relative distances increasing and decreasing by <math>10^{-21}</math> or less. Data analysis methods routinely make use of the fact that these linearized waves can be [[Fourier decomposition|Fourier decomposed]].<ref>For example {{Harvnb|Jaranowski|Królak|2005}}</ref>

Some exact solutions describe gravitational waves without any approximation, e.g., a wave train traveling through empty space<ref>{{Harvnb|Rindler|2001|loc=ch. 13}}</ref> or [[Gowdy universe]]s, varieties of an expanding cosmos filled with gravitational waves.<ref>{{Harvnb|Gowdy|1971}}, {{Harvnb|Gowdy|1974}}</ref> But for gravitational waves produced in astrophysically relevant situations, such as the merger of two black holes, numerical methods are presently the only way to construct appropriate models.<ref>See {{Harvnb|Lehner|2002}} for a brief introduction to the methods of numerical relativity, and {{Harvnb|Seidel|1998}} for the connection with gravitational wave astronomy</ref>