What are Gravitational Waves?

Gravitational waves are 'ripples' in the fabric of space-time caused by some of the most violent and energetic processes in the Universe. Albert Einstein predicted the existence of gravitational waves in 1916 in his general theory of relativity. Einstein's mathematics showed that massive accelerating objects (such as neutron stars or black holes orbiting each other) would disrupt space-time in such a way that 'waves' of distorted space would radiate from the source (like the movement of waves away from a stone thrown into a pond). Furthermore, these ripples would travel at the speed of light through the Universe, carrying with them information about their cataclysmic origins, as well as invaluable clues to the nature of gravity itself.

The strongest gravitational waves are produced by catastrophic events such as colliding black holes, the collapse of stellar cores (supernovae), coalescing neutron stars or white dwarf stars, the slightly wobbly rotation of neutron stars that are not perfect spheres, and the remnants of gravitational radiation created by the birth of the Universe itself.

Though gravitational waves were predicted to exist in 1916, actual proof of their existence wouldn't arrive until 1974, 20 years after Einstein's death. In that year, two astronomers working at the Arecibo Radio Observatory in Puerto Rico discovered a binary pulsar--two extremely dense and heavy stars in orbit around each other. This was exactly the type of system that, according to general relativity, should radiate gravitational waves. Knowing that this discovery could be used to test Einstein's audacious prediction, astronomers began measuring how the period of the stars' orbits changed over time.

 After eight years of observations, it was determined that the stars were getting closer to each other at precisely the rate predicted by general relativity. This system has now been monitored for over 40 years and the observed changes in the orbit agree so well with general relativity, there is no doubt that it is emitting gravitational waves.

Since then, many astronomers have studied the timing of pulsar radio emissions and found similar effects, further confirming the existence of gravitational waves. But these confirmations had always come indirectly or mathematically and not through actual 'physical' contact. 

That was the case up until September 14, 2015, when LIGO, for the first time, physically sensed  distortions in spacetime itself caused by passing gravitational waves generated by two colliding black holes nearly 1.3 billion light years away! LIGO and its discovery will go down in history as one of the greatest human scientific achievements.

Lucky for us here on Earth, while the origins of gravitational waves can be extremely violent, by the time the waves reach the Earth they are millions of times smaller and less disruptive. In fact, by the time gravitational waves from the first detection reached LIGO, the amount of space-time wobbling they generated was thousands of times smaller than the nucleus of an atom!

I short this all stuff is entirely dependent on theory of relativity. Equation for relativity is .

General Introduction:

In Einstein's theory of general 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 corresponding to that of the wave. This occurs despite such free objects never being subjected to an unbalanced force. The magnitude of this effect decreases proportional 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.

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 HzGravitational waves can penetrate regions of space that electromagnetic waves cannot. It is hypothesized that they will be able to allow the observation of the merger of black holes and 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 more thoroughly test the general theory of relativity.

Gravitational waves are constantly passing Earth; however, even the strongest have a miniscule 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 lightyears, as a ripple in spacetime that changed the length of a 4-km LIGO arm by a ten 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 completely undetectable on Earth, by any means other than 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, for example, 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 and 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 polarization of a gravitational wave are at 45 degrees, 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 polarization of gravitational waves may also be expressed in terms of circularly polarized waves. Gravitational waves are polarized because of the nature of their sources.

Sources

 

n general terms, gravitational waves are radiated by objects whose motion involves acceleration, 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 in a quasi-Keplerian planar orbit (basically, as a planet would orbit the Sun) will radiate.
• A spinning non-axisymmetric planetoid — say with a large bump or dimple on the equator — willradiate.
• 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 ofconservation 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 third 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.

Properties and behaviour

Energy, momentum, and angular momentum carried by gravitational waves

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 and blueshifting

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

At present, and unlike all other known forces in the universe, no "force carrying" particle has been identified as mediating gravitational interactions.

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 reconciliation yet exists between general relativity which describes gravity, and the Standard Model which describes all other fundamental forces. (For scientific models which attempt to reconcile these, see quantum gravity).

If such a particle exists, it is expected to be mass-less (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 mass-less spin-2 particle were ever discovered, it would be likely to be the graviton without further distinction from other mass-less spin-2 particles. Such a discovery would unite quantum theory with gravity.

Absorption, re-emission, refraction (lensing), superposition, and other wave effects

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 before space became "transparent"; observations based upon light, radio waves, and other electromagnetic radiation further back into time is limited or unavailable. Therefore, gravitational waves are expected to have the potential to open a new means of observation to 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.

In the case of GW150914, only two detectors were operating at the time of the event, therefore, the direction is not so precisely defined and it could lie anywhere within an arc-shaped region of space rather than being identified as a single point.