Editing Gravitational wave (section)

==Sources==
[[File:The Gravitational wave spectrum Sources and Detectors.jpg|thumb|right|upright=2|The gravitational wave spectrum with sources and detectors. ''Credit: NASA Goddard Space Flight Center''<ref>{{cite web|title=Gravitational Astrophysics Laboratory|url=http://science.gsfc.nasa.gov/663/research/index.html|website=science.gsfc/nasa.gov|access-date=20 September 2016}}</ref>]]
In general terms, gravitational waves are radiated by large, coherent motions of immense mass, especially in regions where gravity is so strong that [[Newtonian gravity]] begins to fail.<ref>{{Cite book |last=Thorne |first=Kip S. |title=Black holes and time warps: Einstein's outrageous legacy |date=1994 |publisher=Norton |isbn=978-0-393-31276-8 |series=The Commonwealth Fund Book Program |location=New York London}}</ref>{{rp|380}}

The effect does not occur in a purely spherically symmetric system.<ref name=Penrose-1965>{{Cite journal |last=Penrose |first=Roger |date=1965-01-18 |title=Gravitational Collapse and Space-Time Singularities |url=https://link.aps.org/doi/10.1103/PhysRevLett.14.57 |journal=Physical Review Letters |language=en |volume=14 |issue=3 |pages=57–59 |doi=10.1103/PhysRevLett.14.57 |bibcode=1965PhRvL..14...57P |issn=0031-9007 |quote=Unfortunately, this precludes any detailed discussion of gravitational radiation —which requires at least a quadripole structure.}}</ref> A simple example of this principle is a spinning [[dumbbell]]. If the dumbbell spins around its axis of symmetry, it will not radiate gravitational waves; if it tumbles end over end, as in the case of two planets orbiting each other, it will radiate gravitational waves. The heavier the dumbbell, and the faster it tumbles, the greater is the gravitational radiation it will give off. In an extreme case, such as when the two weights of the dumbbell are massive stars like neutron stars or black holes, orbiting each other quickly, then significant amounts of gravitational radiation would be given off.

Some more detailed examples:
* Two objects orbiting each other, as a planet would orbit the Sun, ''will'' radiate.
* A spinning non-axisymmetric planetoid{{snd}} say with a large bump or dimple on the equator{{snd}} ''will'' radiate.
* A [[supernova]] ''will'' radiate except in the unlikely event that the explosion is perfectly symmetric.
* An isolated non-spinning solid object moving at a constant velocity ''will not'' radiate. This can be regarded as a consequence of the principle of [[Law of conservation of linear momentum|conservation of linear momentum]].
* A spinning disk ''will not'' radiate. This can be regarded as a consequence of the principle of [[conservation of angular momentum]]. However, it ''will'' show [[Gravitoelectromagnetism|gravitomagnetic]] effects.
* A spherically pulsating spherical star (non-zero monopole moment or [[mass]], but zero quadrupole moment) ''will not'' radiate, in agreement with [[Birkhoff's theorem (relativity)|Birkhoff's theorem]].

More technically, the second time derivative of the [[quadrupole formula|quadrupole moment]] (or the ''l''-th time derivative of the ''l''-th [[multipole expansion|multipole moment]]) of an isolated system's [[stress–energy tensor]] must be non-zero in order for it to emit gravitational radiation. This is analogous to the changing dipole moment of charge or current that is necessary for the emission of [[electromagnetic radiation]].

===Binaries===
{{See also|Two-body problem in general relativity}}
[[File:orbit2.gif|thumb|Two stars of dissimilar mass are in [[circular orbits]]. Each revolves about their common [[center of mass]] (denoted by the small red cross) in a circle with the larger mass having the smaller orbit.]]
[[File:orbit1.gif|thumb|Two stars of similar mass in circular orbits about their center of mass]]
[[File:orbit5.gif|thumb|Two stars of similar mass in highly [[elliptical orbit]]s about their center of mass]]

Gravitational waves carry energy away from their sources and, in the case of orbiting bodies, this is associated with an in-spiral or decrease in orbit.<ref>{{Cite journal |last1=Peters |first1=P.C. |last2=Mathews |first2=J. |date=1963-07-01 |title=Gravitational Radiation from Point Masses in a Keplerian Orbit |journal=Physical Review |volume=131 |issue=1 |pages=435–40 |bibcode=1963PhRv..131..435P |doi=10.1103/PhysRev.131.435 |issn=0031-899X}}</ref><ref>{{cite journal|last=Peters|first=P.|title=Gravitational Radiation and the Motion of Two Point Masses|journal=Physical Review|volume=136|issue=4B|pages=B1224–32|doi=10.1103/PhysRev.136.B1224|bibcode=1964PhRv..136.1224P |date=1964|url=https://thesis.library.caltech.edu/4296/1/Peters_pc_1964.pdf}}</ref> Imagine for example a simple system of two masses{{snd}} such as the Earth–Sun system{{snd}} moving slowly compared to the speed of light in circular orbits. Assume that these two masses orbit each other in a circular orbit in the ''x''–''y'' plane. To a good approximation, the masses follow simple Keplerian [[orbit]]s. However, such an orbit represents a changing [[Quadrupole#Gravitational quadrupole|quadrupole moment]]. That is, the system will give off gravitational waves.

In theory, the loss of energy through gravitational radiation could eventually drop the Earth into the [[Sun]]. However, the total energy of the Earth orbiting the Sun ([[kinetic energy]] + [[gravitational potential energy]]) is about 1.14{{e|36}} [[joules]] of which only 200 [[watt]]s (joules per second) is lost through gravitational radiation, leading to a [[orbital decay|decay in the orbit]] by about 1{{e|-15}} meters per day or roughly the diameter of a [[proton]]. At this rate, it would take the Earth approximately 3{{e|13}} times more than the current [[age of the universe]] to spiral onto the Sun. This estimate overlooks the decrease in ''r'' over time, but the radius varies only slowly for most of the time and plunges at later stages, as <math>r(t)=r_0\left(1-\frac{t}{t_\text{coalesce}} \right)^{1/4},</math> with <math>r_0</math> the initial radius and <math>t_\text{coalesce}</math> the total time needed to fully coalesce.<ref>{{Cite book|last=Maggiore, Michele|title=Gravitational Waves |volume=1, Theory and Experiments|date=2007|publisher=Oxford University Press|isbn=978-0-19-152474-5|location=Oxford|oclc=319064125}}</ref>

More generally, the rate of orbital decay can be approximated by<ref name="Gravitational Radiation">{{cite web|url=http://www.eftaylor.com/exploringblackholes/GravWaves150909v1.pdf|archive-url=https://web.archive.org/web/20160129142844/http://www.eftaylor.com/exploringblackholes/GravWaves150909v1.pdf|archive-date=29 January 2016|title=Chapter 16 {{sic|nolink=y|reason=error in source|Gravity}} Waves|work=AW Physics Macros|date=9 September 2015}}</ref>
:<math>\frac{\mathrm{d}r}{\mathrm{d}t} = - \frac{64}{5}\, \frac{G^3}{c^5}\, \frac{(m_1m_2)(m_1+m_2)}{r^3}\ , </math>
where ''r'' is the separation between the bodies, ''t'' time, ''G'' the [[gravitational constant]], ''c'' the [[speed of light]], and ''m''<sub>1</sub> and ''m''<sub>2</sub> the masses of the bodies. This leads to an expected time to merger of
<ref name="Gravitational Radiation"/>
:<math>t= \frac{5}{256}\, \frac{c^5}{G^3}\, \frac{r^4}{(m_1m_2)(m_1+m_2)}. </math>

====Compact binaries====
[[Compact star]]s like [[white dwarf]]s and [[neutron star]]s can be constituents of binaries. For example, a pair of [[solar mass]] neutron stars in a circular orbit at a separation of 1.89{{e|8}} m (189,000&nbsp;km) has an orbital period of 1,000 seconds, and an expected lifetime of 1.30{{e|13}} seconds or about 414,000 years. Such a system could be observed by [[Laser Interferometer Space Antenna|LISA]] if it were not too far away. A far greater number of white dwarf binaries exist with orbital periods in this range. White dwarf binaries have [[Solar mass|masses in the order of the Sun]], and diameters in the order of the Earth. They cannot get much closer together than 10,000&nbsp;km before they will [[Stellar collision|merge]] and explode in a [[Type Ia supernova#Double degenerate progenitors|supernova]] which would also end the emission of gravitational waves. Until then, their gravitational radiation would be comparable to that of a neutron star binary.

[[File:Artist’s impression of merging neutron stars.jpg|thumb|Artist's impression of merging neutron stars, a source of gravitational waves<ref>{{cite web|title=ESO Telescopes Observe First Light from Gravitational Wave Source – Merging neutron stars scatter gold and platinum into space|url=https://www.eso.org/public/news/eso1733/|website=eso.org|access-date=18 October 2017}}</ref>]]
When the orbit of a neutron star binary has decayed to 1.89{{e|6}} m (1890&nbsp;km), its remaining lifetime is about 130,000 seconds or 36 hours. The orbital frequency will vary from 1 orbit per second at the start, to 918 orbits per second when the orbit has shrunk to 20&nbsp;km at merger. The majority of gravitational radiation emitted will be at twice the orbital frequency. Just before merger, the inspiral could be observed by LIGO if such a binary were close enough. LIGO has only a few minutes to observe this merger out of a total orbital lifetime that may have been billions of years. In August 2017, LIGO and Virgo observed the first binary neutron star inspiral in [[GW170817]], and 70 observatories collaborated to detect the electromagnetic counterpart, a [[kilonova]] in the galaxy [[NGC 4993]], 40 [[megaparsec]]s away, emitting a short [[gamma ray burst]] ([[GRB 170817A]]) seconds after the merger, followed by a longer optical transient ([[AT 2017gfo]]) powered by [[r-process]] nuclei. Advanced LIGO detectors should be able to detect such events up to 200 megaparsecs away; at this range, around 40 detections per year would be expected.<ref>{{citation|title=LIGO Scientific Collaboration – FAQ; section: 'Do we expect LIGO's advanced detectors to make a discovery, then?' and 'What's so different about LIGO's advanced detectors?' |url=http://ligo.org/science/faq.php |access-date=14 February 2016}}</ref>

===Black hole binaries===
{{Main|Binary black hole}}
Black hole binaries emit gravitational waves during their in-spiral, [[Stellar collision|merger]], and ring-down phases. Hence, in the early 1990s the physics community rallied around a concerted effort to predict the waveforms of gravitational waves from these systems with the [[Binary Black Hole Grand Challenge Alliance]].<ref>{{Cite journal |last1=Thorne |first1=Kip |date=2018-12-18 |title=Nobel Lecture: LIGO and gravitational waves III |journal=Rev. Mod. Phys. |volume=90 |issue=40503 |page=040503 |doi=10.1103/RevModPhys.90.040503 |bibcode=2018RvMP...90d0503T |s2cid=125431568 |doi-access=free }}</ref> The largest amplitude of emission occurs during the merger phase, which can be modeled with the techniques of numerical relativity.<ref name="Pretorius2005">{{cite journal|last1=Pretorius|first1=Frans|title=Evolution of Binary Black-Hole Spacetimes|journal=Physical Review Letters|volume=95|issue=12|page=121101|year=2005|issn=0031-9007|doi=10.1103/PhysRevLett.95.121101 |pmid=16197061 |arxiv=gr-qc/0507014 |bibcode=2005PhRvL..95l1101P |s2cid=24225193}}</ref><ref name="CampanelliLousto2006">{{cite journal |last1=Campanelli |first1=M. |author-link=Manuela Campanelli (scientist) |last2=Lousto |first2=C.O. |author-link2=Carlos Lousto |last3=Marronetti |first3=P. |last4=Zlochower |first4=Y. |year=2006 |title=Accurate Evolutions of Orbiting Black-Hole Binaries without Excision |journal=Physical Review Letters |volume=96 |issue=11 |page=111101 |arxiv=gr-qc/0511048 |bibcode=2006PhRvL..96k1101C |doi=10.1103/PhysRevLett.96.111101 |issn=0031-9007 |pmid=16605808 |s2cid=5954627}}</ref><ref name="BakerCentrella2006">{{cite journal|last1=Baker|first1=John G.|last2=Centrella|first2=Joan|author2-link=Joan Centrella |last3=Choi|first3=Dae-Il|last4=Koppitz|first4=Michael|last5=van Meter|first5=James|title=Gravitational-Wave Extraction from an Inspiraling Configuration of Merging Black Holes|journal=Physical Review Letters|volume=96|issue=11|page=111102|year=2006|issn=0031-9007|doi=10.1103/PhysRevLett.96.111102|pmid=16605809 |arxiv=gr-qc/0511103 |bibcode=2006PhRvL..96k1102B |s2cid=23409406}}</ref> The first direct detection of gravitational waves, [[GW150914]], came from the merger of two black holes.

===Supernova===
{{Main|Supernova}}
A supernova is a [[transient astronomical event]] that occurs during the last stellar evolutionary stages of a massive star's life, whose dramatic and catastrophic destruction is marked by one final titanic explosion. This explosion can happen in one of many ways, but in all of them a significant proportion of the matter in the star is blown away into the surrounding space at extremely high velocities (up to 10% of the speed of light). Unless there is perfect spherical symmetry in these explosions (i.e., unless matter is spewed out evenly in all directions), there will be gravitational radiation from the explosion. This is because gravitational waves are [[Quadrupole formula|generated by a changing quadrupole moment]], which can happen only when there is asymmetrical movement of masses. Since the exact mechanism by which supernovae take place is not fully understood, it is not easy to model the gravitational radiation emitted by them.

===Spinning neutron stars===
As noted above, a mass distribution will emit gravitational radiation only when there is spherically asymmetric motion among the masses. A [[Pulsar|spinning neutron star]] will generally emit no gravitational radiation because neutron stars are highly dense objects with a strong gravitational field that keeps them almost perfectly spherical. In some cases, however, there might be slight deformities on the surface called "mountains", which are bumps extending no more than 10 centimeters (4 inches) above the surface,<ref>{{Cite web|url=http://www.space.com/6682-neutron-star-crust-stronger-steel.html|title=Neutron Star Crust Is Stronger than Steel|website=[[Space.com]]|date=18 May 2009|access-date=2016-07-01}}</ref> that make the spinning spherically asymmetric. This gives the star a quadrupole moment that changes with time, and it will emit gravitational waves until the deformities are smoothed out.

===Cosmological===
{{Main|inflation (cosmology)}}

Gravitational waves from the early universe could provide a unique probe for cosmology. Because these wave interact very weakly with matter they would propagate freely from very early time when other signals are trapped by the large density of energy. If this gravitational radiation could be detected today it would be [[gravitational wave background]] complementary to the [[cosmic microwave background]] data.<ref name=Caprini-2018/>