Gravitational waves are disturbances in the
curvature (fabric) of spacetime, generated
by accelerated masses, that propagate as waves
outward from their source at the speed of
light. They were proposed by Henri Poincaré
in 1905 and subsequently predicted in 1916
by Albert Einstein on the basis of his general
theory of relativity. Gravitational waves
transport energy as gravitational radiation,
a form of radiant energy similar to electromagnetic
radiation. Newton's law of universal gravitation,
part of classical mechanics, does not provide
for their existence, since that law is predicated
on the assumption that physical interactions
propagate instantaneously (at infinite speed)—showing
one of the ways the methods of classical physics
are unable to explain phenomena associated
with relativity.
Gravitational-wave astronomy is a branch of
observational astronomy that uses gravitational
waves to collect observational data about
sources of detectable gravitational waves
such as binary star systems composed of white
dwarfs, neutron stars, and black holes; and
events such as supernovae, and the formation
of the early universe shortly after the Big
Bang.
In 1993, Russell A. Hulse and Joseph H. Taylor,
Jr. received the Nobel Prize in Physics for
the discovery and observation of the Hulse-Taylor
binary pulsar, which offered the first indirect
evidence of the existence of gravitational
waves.On 11 February 2016, the LIGO and Virgo
Scientific Collaboration announced they had
made the first direct observation of gravitational
waves. The observation was made five months
earlier, on 14 September 2015, using the Advanced
LIGO detectors. The gravitational waves originated
from a pair of merging black holes. After
the initial announcement the LIGO instruments
detected two more confirmed, and one potential,
gravitational wave events. In August 2017,
the two LIGO instruments and the Virgo instrument
observed a fourth gravitational wave from
merging black holes, and a fifth gravitational
wave from a binary neutron star merger. Several
other gravitational wave detectors are planned
or under construction.In 2017, the Nobel Prize
in Physics was awarded to Rainer Weiss, Kip
Thorne and Barry Barish for their role in
the direct detection of gravitational waves.
== Introduction ==
In Einstein's general theory of relativity,
gravity is treated as a phenomenon resulting
from the curvature of spacetime. This curvature
is caused by the presence of mass. Generally,
the more mass that is contained within a given
volume of space, the greater the curvature
of spacetime will be at the boundary of its
volume. As objects with mass move around in
spacetime, the curvature changes to reflect
the changed locations of those objects. In
certain circumstances, accelerating objects
generate changes in this curvature, which
propagate outwards at the speed of light in
a wave-like manner. These propagating phenomena
are known as gravitational waves.
As a gravitational wave passes an observer,
that observer will find spacetime distorted
by the effects of strain. Distances between
objects increase and decrease rhythmically
as the wave passes, at a frequency equal to
that of the wave. This occurs despite such
free objects never being subjected to an unbalanced
force. The magnitude of this effect decreases
in proportion to the inverse distance from
the source. Inspiraling binary neutron stars
are predicted to be a powerful source of gravitational
waves as they coalesce, due to the very large
acceleration of their masses as they orbit
close to one another. However, due to the
astronomical distances to these sources, the
effects when measured on Earth are predicted
to be very small, having strains of less than
1 part in 1020. Scientists have demonstrated
the existence of these waves with ever more
sensitive detectors. The most sensitive detector
accomplished the task possessing a sensitivity
measurement of about one part in 5×1022 (as
of 2012) provided by the LIGO and VIRGO observatories.
A space based observatory, the Laser Interferometer
Space Antenna, is currently under development
by ESA.
Gravitational waves can penetrate regions
of space that electromagnetic waves cannot.
They are able to allow the observation of
the merger of black holes and possibly other
exotic objects in the distant Universe. Such
systems cannot be observed with more traditional
means such as optical telescopes or radio
telescopes, and so gravitational wave astronomy
gives new insights into the working of the
Universe. In particular, gravitational waves
could be of interest to cosmologists as they
offer a possible way of observing the very
early Universe. This is not possible with
conventional astronomy, since before recombination
the Universe was opaque to electromagnetic
radiation. Precise measurements of gravitational
waves will also allow scientists to test more
thoroughly the general theory of relativity.
In principle, gravitational waves could exist
at any frequency. However, very low frequency
waves would be impossible to detect and there
is no credible source for detectable waves
of very high frequency. Stephen Hawking and
Werner Israel list different frequency bands
for gravitational waves that could plausibly
be detected, ranging from 10−7 Hz up to
1011 Hz.
== History ==
The possibility of gravitational waves was
discussed in 1893 by Oliver Heaviside using
the analogy between the inverse-square law
in gravitation and electricity. In 1905, Henri
Poincaré proposed gravitational waves, emanating
from a body and propagating at the speed of
light, as being required by the Lorentz transformations
and suggested that, in analogy to an accelerating
electrical charge producing electromagnetic
waves, accelerated masses in a relativistic
field theory of gravity should produce gravitational
waves. When Einstein published his general
theory of relativity in 1915, he was skeptical
of Poincaré's idea since the theory implied
there were no "gravitational dipoles". Nonetheless,
he still pursued the idea and based on various
approximations came to the conclusion there
must, in fact, be three types of gravitational
waves (dubbed longitudinal-longitudinal, transverse-longitudinal,
and transverse-transverse by Hermann Weyl).However,
the nature of Einstein's approximations led
many (including Einstein himself) to doubt
the result. In 1922, Arthur Eddington showed
that two of Einstein's types of waves were
artifacts of the coordinate system he used,
and could be made to propagate at any speed
by choosing appropriate coordinates, leading
Eddington to jest that they "propagate at
the speed of thought". This also cast doubt
on the physicality of the third (transverse-transverse)
type that Eddington showed always propagate
at the speed of light regardless of coordinate
system. In 1936, Einstein and Nathan Rosen
submitted a paper to Physical Review in which
they claimed gravitational waves could not
exist in the full general theory of relativity
because any such solution of the field equations
would have a singularity. The journal sent
their manuscript to be reviewed by Howard
P. Robertson, who anonymously reported that
the singularities in question were simply
the harmless coordinate singularities of the
employed cylindrical coordinates. Einstein,
who was unfamiliar with the concept of peer
review, angrily withdrew the manuscript, never
to publish in Physical Review again. Nonetheless,
his assistant Leopold Infeld, who had been
in contact with Robertson, convinced Einstein
that the criticism was correct, and the paper
was rewritten with the opposite conclusion
and published elsewhere.In 1956, Felix Pirani
remedied the confusion caused by the use of
various coordinate systems by rephrasing the
gravitational waves in terms of the manifestly
observable Riemann curvature tensor. At the
time this work was mostly ignored because
the community was focused on a different question:
whether gravitational waves could transmit
energy. This matter was settled by a thought
experiment proposed by Richard Feynman during
the first "GR" conference at Chapel Hill in
1957. In short, his argument known as the
"sticky bead argument" notes that if one takes
a rod with beads then the effect of a passing
gravitational wave would be to move the beads
along the rod; friction would then produce
heat, implying that the passing wave had done
work. Shortly after, Hermann Bondi, a former
gravitational wave skeptic, published a detailed
version of the "sticky bead argument".After
the Chapel Hill conference, Joseph Weber started
designing and building the first gravitational
wave detectors now known as Weber bars. In
1969, Weber claimed to have detected the first
gravitational waves, and by 1970 he was "detecting"
signals regularly from the Galactic Center;
however, the frequency of detection soon raised
doubts on the validity of his observations
as the implied rate of energy loss of the
Milky Way would drain our galaxy of energy
on a timescale much shorter than its inferred
age. These doubts were strengthened when,
by the mid-1970s, repeated experiments from
other groups building their own Weber bars
across the globe failed to find any signals,
and by the late 1970s general consensus was
that Weber's results were spurious.In the
same period, the first indirect evidence for
the existence of gravitational waves was discovered.
In 1974, Russell Alan Hulse and Joseph Hooton
Taylor, Jr. discovered the first binary pulsar,
a discovery that earned them the 1993 Nobel
Prize in Physics. Pulsar timing observations
over the next decade showed a gradual decay
of the orbital period of the
Hulse-Taylor pulsar that matched the loss
of energy and angular momentum in gravitational
radiation predicted by general relativity.This
indirect detection of gravitational waves
motivated further searches despite Weber's
discredited result. Some groups continued
to improve Weber's original concept, while
others pursued the detection of gravitational
waves using laser interferometers. The idea
of using a laser interferometer to detect
gravitational waves seems to have been floated
by various people independently, including
M. E. Gertsenshtein and V. I. Pustovoit in
1962, and Vladimir B. Braginskiĭ in 1966.
The first prototypes were developed in the
1970s by Robert L. Forward and Rainer Weiss.
In the decades that followed, ever more sensitive
instruments were constructed, culminating
in the construction of GEO600, LIGO, and Virgo.After
years of producing null results improved detectors
became operational in 2015 - LIGO made the
first direct detection of gravitational waves
on 14 September 2015. It was inferred that
the signal, dubbed GW150914, originated from
the merger of two black holes with masses
36+5−4 M⊙ and 29+4−4 M⊙, resulting
in a 62+4−4 M⊙ black hole. This suggested
that the gravitational wave signal carried
the energy of roughly three solar masses,
or about 5 x 1047 joules.A year earlier it
appeared LIGO might have been beaten to the
punch when the BICEP2 claimed that they had
detected the imprint of gravitational waves
in the cosmic microwave background. However,
they were later forced to retract their result.In
2017, the Nobel Prize in Physics was awarded
to Rainer Weiss, Kip Thorne and Barry Barish
for their role in the detection of gravitational
waves.
== Effects of passing ==
Gravitational waves are constantly passing
Earth; however, even the strongest have a
minuscule effect and their sources are generally
at a great distance. For example, the waves
given off by the cataclysmic final merger
of GW150914 reached Earth after travelling
over a billion light-years, as a ripple in
spacetime that changed the length of a 4-km
LIGO arm by a thousandth of the width of a
proton, proportionally equivalent to changing
the distance to the nearest star outside the
Solar System by one hair's width. This tiny
effect from even extreme gravitational waves
makes them observable on Earth only with the
most sophisticated detectors.
The effects of a passing gravitational wave,
in an extremely exaggerated form, can be visualized
by imagining a perfectly flat region of spacetime
with a group of motionless test particles
lying in a plane, e.g. the surface of a computer
screen. As a gravitational wave passes through
the particles along a line perpendicular to
the plane of the particles, i.e. following
the observer's line of vision into the screen,
the particles will follow the distortion in
spacetime, oscillating in a "cruciform" manner,
as shown in the animations. The area enclosed
by the test particles does not change and
there is no motion along the direction of
propagation.The oscillations depicted in the
animation are exaggerated for the purpose
of discussion — in reality a gravitational
wave has a very small amplitude (as formulated
in linearized gravity). However, they help
illustrate the kind of oscillations associated
with gravitational waves as produced by a
pair of masses in a circular orbit. In this
case the amplitude of the gravitational wave
is constant, but its plane of polarization
changes or rotates at twice the orbital rate,
so the time-varying gravitational wave size,
or 'periodic spacetime strain', exhibits a
variation as shown in the animation. If the
orbit of the masses is elliptical then the
gravitational wave's amplitude also varies
with time according to Einstein's quadrupole
formula.As with other waves, there are a number
of characteristics used to describe a gravitational
wave:
Amplitude: Usually denoted h, this is the
size of the wave — the fraction of stretching
or squeezing in the animation. The amplitude
shown here is roughly h = 0.5 (or 50%). Gravitational
waves passing through the Earth are many sextillion
times weaker than this — h ≈ 10−20.
Frequency: Usually denoted f, this is the
frequency with which the wave oscillates (1
divided by the amount of time between two
successive maximum stretches or squeezes)
Wavelength: Usually denoted λ, this is the
distance along the wave between points of
maximum stretch or squeeze.
Speed: This is the speed at which a point
on the wave (for example, a point of maximum
stretch or squeeze) travels. For gravitational
waves with small amplitudes, this wave speed
is equal to the speed of light (c).The speed,
wavelength, and frequency of a gravitational
wave are related by the equation c = λ f,
just like the equation for a light wave. For
example, the animations shown here oscillate
roughly once every two seconds. This would
correspond to a frequency of 0.5 Hz, and a
wavelength of about 600 000 km, or 47 times
the diameter of the Earth.
In the above example, it is assumed that the
wave is linearly polarized with a "plus" polarization,
written h+. Polarization of a gravitational
wave is just like polarization of a light
wave except that the polarizations of a gravitational
wave are 45 degrees apart, as opposed to 90
degrees. In particular, in a "cross"-polarized
gravitational wave, h×, the effect on the
test particles would be basically the same,
but rotated by 45 degrees, as shown in the
second animation. Just as with light polarization,
the polarizations of gravitational waves may
also be expressed in terms of circularly polarized
waves. Gravitational waves are polarized because
of the nature of their source.
== Sources ==
In general terms, gravitational waves are
radiated by objects whose motion involves
acceleration and its change, provided that
the motion is not perfectly spherically symmetric
(like an expanding or contracting sphere)
or rotationally symmetric (like a spinning
disk or sphere). 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 — say
with a large bump or dimple on the equator
— 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 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 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.More technically, the second
time derivative of the quadrupole moment (or
the l-th time derivative of the l-th 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 ===
Gravitational waves carry energy away from
their sources and, in the case of orbiting
bodies, this is associated with an inspiral
or decrease in orbit. Imagine for example
a simple system of two masses — such as
the Earth–Sun system — 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 orbits. However, such an orbit represents
a changing 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
1.14×1036 joules of which only 200 watts
(joules per second) is lost through gravitational
radiation, leading to a decay in the orbit
by about 1×10−15 meters per day or roughly
the diameter of a proton. At this rate, it
would take the Earth approximately 1×1013
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 majority
of the time the bodies are far apart and only
radiating slowly, so the difference is unimportant
in this example.More generally, the rate of
orbital decay can be approximated by
d
r
d
t
=
−
64
5
G
3
c
5
(
m
1
m
2
)
(
m
1
+
m
2
)
r
3
,
{\displaystyle {\frac {\mathrm {d} r}{\mathrm
{d} t}}=-{\frac {64}{5}}\,{\frac {G^{3}}{c^{5}}}\,{\frac
{(m_{1}m_{2})(m_{1}+m_{2})}{r^{3}}}\ ,}
where r is the separation between the bodies,
t time, G the gravitational constant, c the
speed of light, and m1 and m2 the masses of
the bodies. This leads to an expected time
to merger of
t
=
5
256
c
5
G
3
r
4
(
m
1
m
2
)
(
m
1
+
m
2
)
.
{\displaystyle t={\frac {5}{256}}\,{\frac
{c^{5}}{G^{3}}}\,{\frac {r^{4}}{(m_{1}m_{2})(m_{1}+m_{2})}}.}
==== Compact binaries ====
Compact stars like white dwarfs and neutron
stars can be constituents of binaries. For
example, a pair of solar mass neutron stars
in a circular orbit at a separation of 1.89×108
m (189,000 km) has an orbital period of 1,000
seconds, and an expected lifetime of 1.30×1013
seconds or about 414,000 years. Such a system
could be observed by 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 masses in
the order of the Sun, and diameters in the
order of the Earth. They cannot get much closer
together than 10,000 km before they will merge
and explode in a 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.
When the orbit of a neutron star binary has
decayed to 1.89×106 m (1890 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 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. ln 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 megaparsecs 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 detector should be able to detect
such events up to 200 megaparsecs away. Within
this range of the order 40 events are expected
per year.
=== Black hole binaries ===
Black hole binaries emit gravitational waves
during their in-spiral, merger, and ring-down
phases. The largest amplitude of emission
occurs during the merger phase, which can
be modeled with the techniques of numerical
relativity. The first direct detection of
gravitational waves, GW150914, came from the
merger of two black holes.
=== Supernovae ===
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 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 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, 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.
=== Inflation ===
Many models of the Universe suggest that there
was an inflationary epoch in the early history
of the Universe when space expanded by a large
factor in a very short amount of time. If
this expansion was not symmetric in all directions,
it may have emitted gravitational radiation
detectable today as a gravitational wave background.
This background signal is too weak for any
currently operational gravitational wave detector
to observe, and it is thought it may be decades
before such an observation can be made.
== Properties and behaviour ==
=== Energy, momentum, and angular momentum
===
Water waves, sound waves, and electromagnetic
waves are able to carry energy, momentum,
and angular momentum and by doing so they
carry those away from the source. Gravitational
waves perform the same function. Thus, for
example, a binary system loses angular momentum
as the two orbiting objects spiral towards
each other—the angular momentum is radiated
away by gravitational waves.
The waves can also carry off linear momentum,
a possibility that has some interesting implications
for astrophysics. After two supermassive black
holes coalesce, emission of linear momentum
can produce a "kick" with amplitude as large
as 4000 km/s. This is fast enough to eject
the coalesced black hole completely from its
host galaxy. Even if the kick is too small
to eject the black hole completely, it can
remove it temporarily from the nucleus of
the galaxy, after which it will oscillate
about the center, eventually coming to rest.
A kicked black hole can also carry a star
cluster with it, forming a hyper-compact stellar
system. Or it may carry gas, allowing the
recoiling black hole to appear temporarily
as a "naked quasar".
The quasar SDSS J092712.65+294344.0 is thought
to contain a recoiling supermassive black
hole.
=== Redshifting ===
Like electromagnetic waves, gravitational
waves should exhibit shifting of wavelength
due to the relative velocities of the source
and observer, but also due to distortions
of space-time, such as cosmic expansion. This
is the case even though gravity itself is
a cause of distortions of space-time. Redshifting
of gravitational waves is different from redshifting
due to gravity.
=== Quantum gravity, wave-particle aspects,
and graviton ===
In the framework of quantum field theory,
the graviton is the name given to a hypothetical
elementary particle speculated to be the force
carrier that mediates gravity. However the
graviton is not yet proven to exist, and no
scientific model yet exists that successfully
reconciles general relativity, which describes
gravity, and the Standard Model, which describes
all other fundamental forces. Attempts, such
as quantum gravity, have been made, but are
not yet accepted.
If such a particle exists, it is expected
to be massless (because the gravitational
force appears to have unlimited range) and
must be a spin-2 boson. It can be shown that
any massless spin-2 field would give rise
to a force indistinguishable from gravitation,
because a massless spin-2 field must couple
to (interact with) the stress–energy tensor
in the same way that the gravitational field
does; therefore if a massless spin-2 particle
were ever discovered, it would be likely to
be the graviton without further distinction
from other massless spin-2 particles. Such
a discovery would unite quantum theory with
gravity.
=== Significance for study of the early universe
===
Due to the weakness of the coupling of gravity
to matter, gravitational waves experience
very little absorption or scattering, even
as they travel over astronomical distances.
In particular, gravitational waves are expected
to be unaffected by the opacity of the very
early universe. In these early phases, space
had not yet become "transparent," so observations
based upon light, radio waves, and other electromagnetic
radiation that far back into time are limited
or unavailable. Therefore, gravitational waves
are expected in principle to have the potential
to provide a wealth of observational data
about the very early universe.
=== Determining direction of travel ===
The difficulty in directly detecting gravitational
waves, means it is also difficult for a single
detector to identify by itself the direction
of a source. Therefore, multiple detectors
are used, both to distinguish signals from
other "noise" by confirming the signal is
not of earthly origin, and also to determine
direction by means of triangulation. This
technique uses the fact that the waves travel
at the speed of light and will reach different
detectors at different times depending on
their source direction. Although the differences
in arrival time may be just a few milliseconds,
this is sufficient to identify the direction
of the origin of the wave with considerable
precision.
Only in the case of GW170814 were three detectors
operating at the time of the event, therefore,
the direction is precisely defined. The detection
by all three instruments led to a very accurate
estimate of the position of the source, with
a 90% credible region of just 60 deg2, a factor
20 more accurate than before.
== Gravitational wave astronomy ==
During the past century, astronomy has been
revolutionized by the use of new methods for
observing the universe. Astronomical observations
were originally made using visible light.
Galileo Galilei pioneered the use of telescopes
to enhance these observations. However, visible
light is only a small portion of the electromagnetic
spectrum, and not all objects in the distant
universe shine strongly in this particular
band. More useful information may be found,
for example, in radio wavelengths. Using radio
telescopes, astronomers have found pulsars,
quasars, and made other unprecedented discoveries
of objects not formerly known to scientists.
Observations in the microwave band led to
the detection of faint imprints of the Big
Bang, a discovery Stephen Hawking called the
"greatest discovery of the century, if not
all time". Similar advances in observations
using gamma rays, x-rays, ultraviolet light,
and infrared light have also brought new insights
to astronomy. As each of these regions of
the spectrum has opened, new discoveries have
been made that could not have been made otherwise.
Astronomers hope that the same holds true
of gravitational waves.Gravitational waves
have two important and unique properties.
First, there is no need for any type of matter
to be present nearby in order for the waves
to be generated by a binary system of uncharged
black holes, which would emit no electromagnetic
radiation. Second, gravitational waves can
pass through any intervening matter without
being scattered significantly. Whereas light
from distant stars may be blocked out by interstellar
dust, for example, gravitational waves will
pass through essentially unimpeded. These
two features allow gravitational waves to
carry information about astronomical phenomena
heretofore never observed by humans, and as
such represent a revolution in astrophysics.The
sources of gravitational waves described above
are in the low-frequency end of the gravitational-wave
spectrum (10−7 to 105 Hz). An astrophysical
source at the high-frequency end of the gravitational-wave
spectrum (above 105 Hz and probably 1010 Hz)
generates relic gravitational waves that are
theorized to be faint imprints of the Big
Bang like the cosmic microwave background.
At these high frequencies it is potentially
possible that the sources may be "man made"
that is, gravitational waves generated and
detected in the laboratory.A supermassive
black hole, created from the merger of the
black holes at the center of two merging galaxies
detected by the Hubble Space Telescope, is
theorized to have been ejected from the merger
center by gravitational waves.
== Detection ==
=== 
Indirect detection ===
Although the waves from the Earth–Sun system
are minuscule, astronomers can point to other
sources for which the radiation should be
substantial. One important example is the
Hulse–Taylor binary — a pair of stars,
one of which is a pulsar. The characteristics
of their orbit can be deduced from the Doppler
shifting of radio signals given off by the
pulsar. Each of the stars is about 1.4 M☉
and the size of their orbits is about 1/75
of the Earth–Sun orbit, just a few times
larger than the diameter of our own Sun. The
combination of greater masses and smaller
separation means that the energy given off
by the Hulse–Taylor binary will be far greater
than the energy given off by the Earth–Sun
system — roughly 1022 times as much.
The information about the orbit can be used
to predict how much energy (and angular momentum)
would be radiated in the form of gravitational
waves. As the binary system loses energy,
the stars gradually draw closer to each other,
and the orbital period decreases. The resulting
trajectory of each star is an inspiral, a
spiral with decreasing radius. General relativity
precisely describes these trajectories; in
particular, the energy radiated in gravitational
waves determines the rate of decrease in the
period, defined as the time interval between
successive periastrons (points of closest
approach of the two stars). For the Hulse-Taylor
pulsar, the predicted current change in radius
is about 3 mm per orbit, and the change in
the 7.75 hr period is about 2 seconds per
year. Following a preliminary observation
showing an orbital energy loss consistent
with gravitational waves, careful timing observations
by Taylor and Joel Weisberg dramatically confirmed
the predicted period decrease to within 10%.
With the improved statistics of more than
30 years of timing data since the pulsar's
discovery, the observed change in the orbital
period currently matches the prediction from
gravitational radiation assumed by general
relativity to within 0.2 percent. In 1993,
spurred in part by this indirect detection
of gravitational waves, the Nobel Committee
awarded the Nobel Prize in Physics to Hulse
and Taylor for "the discovery of a new type
of pulsar, a discovery that has opened up
new possibilities for the study of gravitation."
The lifetime of this binary system, from the
present to merger is estimated to be a few
hundred million years.Inspirals are very important
sources of gravitational waves. Any time two
compact objects (white dwarfs, neutron stars,
or black holes) are in close orbits, they
send out intense gravitational waves. As they
spiral closer to each other, these waves become
more intense. At some point they should become
so intense that direct detection by their
effect on objects on Earth or in space is
possible. This direct detection is the goal
of several large scale experiments.The only
difficulty is that most systems like the Hulse–Taylor
binary are so far away. The amplitude of waves
given off by the Hulse–Taylor binary at
Earth would be roughly h ≈ 10−26. There
are some sources, however, that astrophysicists
expect to find that produce much greater amplitudes
of h ≈ 10−20. At least eight other binary
pulsars have been discovered.
=== Difficulties ===
Gravitational waves are not easily detectable.
When they reach the Earth, they have a small
amplitude with strain approximates 10−21,
meaning that an extremely sensitive detector
is needed, and that other sources of noise
can overwhelm the signal. Gravitational waves
are expected to have frequencies 10−16 Hz
< f < 104 Hz.
=== Ground-based detectors ===
Though the Hulse–Taylor observations were
very important, they give only indirect evidence
for gravitational waves. A more conclusive
observation would be a direct measurement
of the effect of a passing gravitational wave,
which could also provide more information
about the system that generated it. Any such
direct detection is complicated by the extraordinarily
small effect the waves would produce on a
detector. The amplitude of a spherical wave
will fall off as the inverse of the distance
from the source (the 1/R term in the formulas
for h above). Thus, even waves from extreme
systems like merging binary black holes die
out to very small amplitudes by the time they
reach the Earth. Astrophysicists expect that
some gravitational waves passing the Earth
may be as large as h ≈ 10−20, but generally
no bigger.
==== Resonant antennae ====
A simple device theorised to detect the expected
wave motion is called a Weber bar — a large,
solid bar of metal isolated from outside vibrations.
This type of instrument was the first type
of gravitational wave detector. Strains in
space due to an incident gravitational wave
excite the bar's resonant frequency and could
thus be amplified to detectable levels. Conceivably,
a nearby supernova might be strong enough
to be seen without resonant amplification.
With this instrument, Joseph Weber claimed
to have detected daily signals of gravitational
waves. His results, however, were contested
in 1974 by physicists Richard Garwin and David
Douglass. Modern forms of the Weber bar are
still operated, cryogenically cooled, with
superconducting quantum interference devices
to detect vibration. Weber bars are not sensitive
enough to detect anything but extremely powerful
gravitational waves.MiniGRAIL is a spherical
gravitational wave antenna using this principle.
It is based at Leiden University, consisting
of an exactingly machined 1,150 kg sphere
cryogenically cooled to 20 millikelvins. The
spherical configuration allows for equal sensitivity
in all directions, and is somewhat experimentally
simpler than larger linear devices requiring
high vacuum. Events are detected by measuring
deformation of the detector sphere. MiniGRAIL
is highly sensitive in the 2–4 kHz range,
suitable for detecting gravitational waves
from rotating neutron star instabilities or
small black hole mergers.There are currently
two detectors focused on the higher end of
the gravitational wave spectrum (10−7 to
105 Hz): one at University of Birmingham,
England, and the other at INFN Genoa, Italy.
A third is under development at Chongqing
University, China. The Birmingham detector
measures changes in the polarization state
of a microwave beam circulating in a closed
loop about one meter across. Both detectors
are expected to be sensitive to periodic spacetime
strains of h ~ 2×10−13 /√Hz, given as
an amplitude spectral density. The INFN Genoa
detector is a resonant antenna consisting
of two coupled spherical superconducting harmonic
oscillators a few centimeters in diameter.
The oscillators are designed to have (when
uncoupled) almost equal resonant frequencies.
The system is currently expected to have a
sensitivity to periodic spacetime strains
of h ~ 2×10−17 /√Hz, with an expectation
to reach a sensitivity of h ~ 2×10−20 /√Hz.
The Chongqing University detector is planned
to detect relic high-frequency gravitational
waves with the predicted typical parameters
~1011 Hz (100 GHz) and h ~10−30 to 10−32.
==== Interferometers ====
A more sensitive class of detector uses laser
interferometry to measure gravitational-wave
induced motion between separated 'free' masses.
This allows the masses to be separated by
large distances (increasing the signal size);
a further advantage is that it is sensitive
to a wide range of frequencies (not just those
near a resonance as is the case for Weber
bars). After years of development the first
ground-based interferometers became operational
in 2015. Currently, the most sensitive is
LIGO — the Laser Interferometer Gravitational
Wave Observatory. LIGO has three detectors:
one in Livingston, Louisiana, one at the Hanford
site in Richland, Washington and a third (formerly
installed as a second detector at Hanford)
that is planned to be moved to India. Each
observatory has two light storage arms that
are 4 kilometers in length. These are at 90
degree angles to each other, with the light
passing through 1 m diameter vacuum tubes
running the entire 4 kilometers. A passing
gravitational wave will slightly stretch one
arm as it shortens the other. This is precisely
the motion to which an interferometer is most
sensitive.
Even with such long arms, the strongest gravitational
waves will only change the distance between
the ends of the arms by at most roughly 10−18
m. LIGO should be able to detect gravitational
waves as small as h ~ 5×10−22. Upgrades
to LIGO and Virgo should increase the sensitivity
still further. Another highly sensitive interferometer,
KAGRA, is under construction in the Kamiokande
mine in Japan. A key point is that a tenfold
increase in sensitivity (radius of 'reach')
increases the volume of space accessible to
the instrument by one thousand times. This
increases the rate at which detectable signals
might be seen from one per tens of years of
observation, to tens per year.Interferometric
detectors are limited at high frequencies
by shot noise, which occurs because the lasers
produce photons randomly; one analogy is to
rainfall—the rate of rainfall, like the
laser intensity, is measurable, but the raindrops,
like photons, fall at random times, causing
fluctuations around the average value. This
leads to noise at the output of the detector,
much like radio static. In addition, for sufficiently
high laser power, the random momentum transferred
to the test masses by the laser photons shakes
the mirrors, masking signals of low frequencies.
Thermal noise (e.g., Brownian motion) is another
limit to sensitivity. In addition to these
'stationary' (constant) noise sources, all
ground-based detectors are also limited at
low frequencies by seismic noise and other
forms of environmental vibration, and other
'non-stationary' noise sources; creaks in
mechanical structures, lightning or other
large electrical disturbances, etc. may also
create noise masking an event or may even
imitate an event. All these must be taken
into account and excluded by analysis before
detection may be considered a true gravitational
wave event.
==== Einstein@Home ====
The simplest gravitational waves are those
with constant frequency. The waves given off
by a spinning, non-axisymmetric neutron star
would be approximately monochromatic: a pure
tone in acoustics. Unlike signals from supernovae
of binary black holes, these signals evolve
little in amplitude or frequency over the
period it would be observed by ground-based
detectors. However, there would be some change
in the measured signal, because of Doppler
shifting caused by the motion of the Earth.
Despite the signals being simple, detection
is extremely computationally expensive, because
of the long stretches of data that must be
analysed.
The Einstein@Home project is a distributed
computing project similar to SETI@home intended
to detect this type of gravitational wave.
By taking data from LIGO and GEO, and sending
it out in little pieces to thousands of volunteers
for parallel analysis on their home computers,
Einstein@Home can sift through the data far
more quickly than would be possible otherwise.
=== Space-based interferometers ===
Space-based interferometers, such as LISA
and DECIGO, are also being developed. LISA's
design calls for three test masses forming
an equilateral triangle, with lasers from
each spacecraft to each other spacecraft forming
two independent interferometers. LISA is planned
to occupy a solar orbit trailing the Earth,
with each arm of the triangle being five million
kilometers. This puts the detector in an excellent
vacuum far from Earth-based sources of noise,
though it will still be susceptible to heat,
shot noise, and artifacts caused by cosmic
rays and solar wind.
=== Using pulsar timing arrays ===
Pulsars are rapidly rotating stars. A pulsar
emits beams of radio waves that, like lighthouse
beams, sweep through the sky as the pulsar
rotates. The signal from a pulsar can be detected
by radio telescopes as a series of regularly
spaced pulses, essentially like the ticks
of a clock. GWs affect the time it takes the
pulses to travel from the pulsar to a telescope
on Earth. A pulsar timing array uses millisecond
pulsars to seek out perturbations due to GWs
in measurements of the time of arrival of
pulses to a telescope, in other words, to
look for deviations in the clock ticks. To
detect GWs, pulsar timing arrays search for
a distinct pattern of correlation and anti-correlation
between the time of arrival of pulses from
several pulsars. Although pulsar pulses travel
through space for hundreds or thousands of
years to reach us, pulsar timing arrays are
sensitive to perturbations in their travel
time of much less than a millionth of a second.
The principal source of GWs to which pulsar
timing arrays are sensitive are super-massive
black hole binaries, that form from the collision
of galaxies. In addition to individual binary
systems, pulsar timing arrays are sensitive
to a stochastic background of GWs made from
the sum of GWs from many galaxy mergers. Other
potential signal sources include cosmic strings
and the primordial background of GWs from
cosmic inflation.
Globally there are three active pulsar timing
array projects. The North American Nanohertz
Observatory for Gravitational Waves uses data
collected by the Arecibo Radio Telescope and
Green Bank Telescope. The Australian Parkes
Pulsar Timing Array uses data from the Parkes
radio-telescope. The European Pulsar Timing
Array uses data from the four largest telescopes
in Europe: the Lovell Telescope, the Westerbork
Synthesis Radio Telescope, the Effelsberg
Telescope and the Nancay Radio Telescope.
These three groups also collaborate under
the title of the International Pulsar Timing
Array project.
=== Primordial ===
Primordial gravitational waves are gravitational
waves observed in the cosmic microwave background.
They were allegedly detected by the BICEP2
instrument, an announcement made on 17 March
2014, which was withdrawn on 30 January 2015
("the signal can be entirely attributed to
dust in the Milky Way").
=== LIGO and Virgo observations ===
On 11 February 2016, the LIGO collaboration
announced the first observation of gravitational
waves, from a signal detected at 09:50:45
GMT on 14 September 2015 of two black holes
with masses of 29 and 36 solar masses merging
about 1.3 billion light-years away. During
the final fraction of a second of the merger,
it released more than 50 times the power of
all the stars in the observable universe combined.
The signal increased in frequency from 35
to 250 Hz over 10 cycles (5 orbits) as it
rose in strength for a period of 0.2 second.
The mass of the new merged black hole was
62 solar masses. Energy equivalent to three
solar masses was emitted as gravitational
waves. The signal was seen by both LIGO detectors
in Livingston and Hanford, with a time difference
of 7 milliseconds due to the angle between
the two detectors and the source. The signal
came from the Southern Celestial Hemisphere,
in the rough direction of (but much further
away than) the Magellanic Clouds. The confidence
level of this being an observation of gravitational
waves was 99.99994%.Since then LIGO and Virgo
have reported more gravitational wave observations
from merging black hole binaries.
On 16 October 2017 the LIGO and Virgo collaborations
announced the first ever detection of gravitational
waves originating from the coalescence of
a binary neutron star system. The observation
of the GW170817 transient, which occurred
on 17 August 2017, allowed for constraining
the masses of the neutron stars involved between
0.86 and 2.26 solar masses. Further analysis
allowed a greater restriction of the mass
values to the interval 1.17–1.60 solar masses,
with the total system mass measured to be
2.73–2.78 solar masses. The inclusion of
the Virgo detector in the observation effort
allowed for an improvement of the localization
of the source by a factor of 10. This in turn
facilitated the electromagnetic follow-up
of the event. In contrast to the case of binary
black hole mergers, binary neutron star mergers
were expected to yield an electromagnetic
counterpart, that is, a light signal associated
with the event. A gamma-ray burst (GRB 170817A)
was detected by the Fermi Gamma-ray Space
Telescope, occurring 1.7 seconds after the
gravitational wave transient. The signal,
originating near the galaxy NGC 4993, was
associated with the neutron star merger. This
was corroborated by the electromagnetic follow-up
of the event (AT 2017gfo), involving 70 telescopes
and observatories and yielding observations
over a large region of the electromagnetic
spectrum which further confirmed the neutron
star nature of the merged objects and the
associated kilonova.
== In fiction ==
An episode of the Russian science-fiction
novel Space Apprentice by Arkady and Boris
Strugatsky shows the experiment monitoring
the propagation of gravitational waves at
the expense of annihilating a chunk of asteroid
15 Eunomia the size of Mount Everest.In Stanislaw
Lem's Fiasco, a "gravity gun" or "gracer"
(gravity amplification by collimated emission
of resonance) is used to reshape a collapsar,
so that the protagonists can exploit the extreme
relativistic effects and make an interstellar
journey.
In Greg Egan's Diaspora, the analysis of a
gravitational wave signal from the inspiral
of a nearby binary neutron star reveals that
its collision and merger is imminent, implying
a large gamma-ray burst is going to impact
the Earth.
== See also
