Regarding gravitational waves

Gravitational waves have become a popular topic recently , and this post presents material I have written for an answer at quora.com (with a few modifications).

Gravitational waves are changes in curvature similar to ripples in space-time . They are an indirect result of the special theory theory of relativity , and were explicitly proposed by Einstein in 1916 in the framework of his theory of general relativity . He showed that the acceleration of mass generates gravitational fields which are time-dependent and are capable of transporting energy (as gravitational radiation ) from their source at the speed of light .
Gravitational waves are quadrupolar in nature , whereas electromagnetic waves are dipolar . Oscillating multipole moments of the mass distribution of a system produce gravitational radiation .
Many attempts have been made to detect gravitational waves , but no direct evidence of their existence has been observed until their recent detection in February 2016 .

The Einstein field equations describe the interactions between space-time curvature and mass , as Maxwell’s equations describe and specify the relationship between electric charge and electromagnetic fields .
The field equations have a solution represented by a weak oscillating perturbation to the curvature of space-time , and this solution is a gravitational wave .
These waves can be regarded as an oscillating perturbation to a flat Minkowski space-time metric , or also as a tidal force oscillating between free test masses , or as a strain oscillating in space-time .
More explicitly , one can show that a wave equation represents the solutions in free space for the metric perturbations of a nearly flat space-time , with waves propagating at the speed of light ( this is a weak gravitational field approximation) .
One can take a coordinate system where the metric has components :
g_ {\mu\nu} = \eta_ {\mu\nu} + h_ {\mu\nu}
where
\eta_ {\mu\nu}  is the Minkowski metric in special relativity , and
h mu nu

After some calculations the  solution to Einstein’s equations in free space can be written as :

wave eq

where

hbar mu nu

So the metric perturbations propagate in free space as waves at the speed of light .
A primary example of a source of gravitational waves is a pair of neutron stars , or two black holes , or one of each type of these astrophysical objects .
Observing supernova explosions or the orbital motion of binary pulsars may possibly give and indirect proof of the existence of gravitational waves .
The image below represents gravitational waves generated by two neutron stars orbiting each other (image source : File:Wavy.gif ) :
wavy anim

 

Ways of detecting gravitational waves include resonant mass detectors , free mass detectors , detectors in space , cosmic background measurements , and monitoring pulsar signals .
External disturbances and the effects of thermal noise in the detecting system should be avoided , the possible interaction between detectors and gravitational waves being very weak .
In 1974 Russell Hulse and Joseph Taylor discovered and observed the orbital period of a binary pulsar . They confirmed that the orbit was accelerating at the rate predicted by the emission of gravitational waves according to the theory of general relativity .
The LIGO (Laser Interferometer Gravitational-Wave Observatory) detectors
are used to attempt to observe directly cosmic gravitational waves . They can detect extremely small strains (of the order of  one part in 10²¹ ).
In the quantum theory of gravity , a quantum field whose excitations are gravitons represents the gravitational field .
Gravitons may be regarded as the normal modes of oscillation of a (gravitational) gauge field , produced by a mass current of accelerating masses .
Some (online) links and resources :
Gravitational wave
McGraw-Hill Encyclopedia of Science and Technology , 10th Edition .

To make this answer complete  , it should be noted that the expression gravity waves is also used to refer to waves studied in oceanography , meteorology and fluid dynamics .
Used in this sense , a gravity wave is a liquid surface layer wave controlled by gravity and not by surface tension .
The surface tension of water becomes unimportant at wavelengths greater than a few centimeters . On the ocean surface or interfaces , all significant waves are gravity waves .
In meteorology , gravity waves are transverse atmospheric waves where the restoring force is caused by the effect of gravity on density and pressure fluctuations .
See for example the Wikipedia article Gravity wave .
The expressions gravity waves and gravitational waves are sometimes used interchangeably for both meanings (i.e. for waves related to general relativity and waves related to fluid dynamics) , so this might cause some confusion.

As an update to the information above , something new took place in the history of the detection of gravitational waves on 11 February 2016 .
For the first time, scientists have observed ripples in the fabric of spacetime called gravitational waves, arriving at Earth from a cataclysmic event in the distant universe. This confirms a major prediction of Albert Einstein’s 1915 general theory of relativity and opens an unprecedented new window to the cosmos.[…]
The gravitational waves were detected on Sept. 14, 2015 at 5:51 a.m. EDT (09:51 UTC) by both of the twin Laser Interferometer Gravitational-wave Observatory (LIGO) detectors, located in Livingston, Louisiana, and Hanford, Washington.[…]
Based on the observed signals, LIGO scientists estimate that the black holes for this event were about 29 and 36 times the mass of the sun, and the event took place 1.3 billion years ago. About three times the mass of the sun was converted into gravitational waves in a fraction of a second—with a peak power output about 50 times that of the whole visible universe. […]
The discovery was made possible by the enhanced capabilities of Advanced LIGO, a major upgrade that increases the sensitivity of the instruments compared to the first generation LIGO detectors, enabling a large increase in the volume of the universe probed—and the discovery of gravitational waves during its first observation run.
As and additional note , it is generally preferable to have other precise experiments confirming the detection and presence of gravitational waves.
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