General relativity
$G_{\mu \nu} + \Lambda g_{\mu \nu}= {8\pi G\over c^4} T_{\mu \nu}\,$
Einstein field equations
Introduction to...
Mathematical formulation of...
Phenomena
Kepler problem · Lenses · Waves
Frame-dragging · Geodetic effect
Event horizon · Singularity
Black hole
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 Gravitational Lensing FormalismWeak lensingMicrolensingEinstein ring This box: view • talk • edit

A gravitational lens is formed when the light from a very distant, bright source (such as a quasar) is "bent" around a massive object (such as a cluster of galaxies) between the source object and the observer. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 The Einstein field equations ( EFE) or Einstein's equations are a set of ten equations in Einstein 's theory of General relativity in which the General relativity (GR is a Theory of Gravitation that was developed by Albert Einstein between 1907 and 1915 The mathematics of general relativity refers to various mathematical structures and techniques that are used in studying Albert Einstein 's theory of General The Kepler problem in general relativity involves solving for the motion of two spherical bodies interacting with one another by Gravitation, as described by the theory of In Physics, a gravitational wave is a Fluctuation in the Curvature of Spacetime which propagates as a wave, traveling outward from Albert Einstein 's theory of General relativity predicts that rotating bodies drag Spacetime around themselves in a phenomenon referred to as frame-dragging The geodetic effect represents the effect of the curvature of Spacetime, predicted by General relativity, on a spinning moving body In General relativity, an event horizon is a boundary in Spacetime, an area surrounding a Black hole or a Wormhole, inside which events cannot A gravitational singularity (sometimes spacetime singularity) is approximately a place where quantities which are used to measure the Gravitational field become A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e A gravitational lens is formed when the light from a very distant bright source (such as a Quasar) is "bent" around a massive object (such as a cluster of In General relativity, a point mass deflects a light ray with Impact parameter b~ by an angle \hat{\alpha} = \frac{4GM}{c^2b} While the presence of any mass bends the path of light passing near it this effect rarely produces the giant arcs and multiple images associated with strong gravitational lensing. Gravitational microlensing is an astronomical phenomenon due to the Gravitational lens effect In observational Astronomy an Einstein ring is the deformation of the light from a source (such as a Galaxy or Star) into a ring through Gravitational A quasar (contraction of QUASi-stellAR radio source) is an extremely powerful and distant Active galactic nucleus. Galaxy groups and clusters are the largest Gravitationally bound objects to have arisen thus far in the process of cosmic structure formation The process is known as gravitational lensing, and is one of the predictions of Albert Einstein's general theory of relativity. At its introduction in 1915 the general theory of relativity did not have a solid empirical foundation Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916

Although Orest Chwolson is credited as being the first to discuss the effect in print (in 1924), the effect is more usually associated with Einstein, who published a more famous article on the subject in 1936.

Fritz Zwicky posited in 1937 that the effect could allow galaxy clusters to act as gravitational lenses. Fritz Zwicky ( February 14 1898 &ndash February 8 1974) was an American-based Swiss Astronomer of Bulgarian origin It was not until 1979 that this effect was confirmed by observation of the so-called "Twin Quasar" Q0957+561. The Twin Quasar (Double Quasar or Old Faithful is also known as Q0957+561, or QSO 0957+561.

Description

Bending light around a massive object from a distant source. The orange arrows show the apparent position of the background source. The white arrows show the path of the light from the true position of the source.

The gravity from a massive object (such as a galaxy cluster or black hole) can warp space-time, bending everything in it - including the paths followed by light rays from a bright background source. Gravitation is a natural Phenomenon by which objects with Mass attract one another Galaxy groups and clusters are the largest Gravitationally bound objects to have arisen thus far in the process of cosmic structure formation A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 This alters the time taken for the light to reach an observer, and can both magnify and distort the apparent image of the background source.

Unlike an optical lens, maximum 'bending' occurs closest to, and minimum 'bending' furthest from, the center of a gravitational lens. A lens is an optical device with perfect or approximate Axial symmetry which transmits and refracts Light, converging or diverging Consequently, a gravitational lens has no single focal point, but a focal line instead. In Geometrical optics, a focus, also called an image point, is the point where Light rays originating from a point on the object converge. If the source, massive lensing object, and observer lie in a straight line, the source will appear as a ring behind the massive object. This phenomenon was first mentioned in 1924 by the St. Petersburg physicist Orest Chwolson [1], and quantified by Albert Einstein in 1936. Saint Petersburg ( tr: Sankt-Peterburg,) is a city and a federal subject of Russia located on the Neva River Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical Year 1936 ( MCMXXXVI) was a Leap year starting on Wednesday (link will display the full calendar of the Gregorian calendar. It is usually referred to in the literature as an Einstein ring, since Chwolson did not concern himself with the flux or radius of the ring image. In observational Astronomy an Einstein ring is the deformation of the light from a source (such as a Galaxy or Star) into a ring through Gravitational More commonly, if the lens is slightly misaligned, the source will resemble partial arcs around the lens. The observer may see multiple images of the same source; the number and shape of these depends upon the relative positions of the source, lens, and observer, and the shape of the gravitational well of the lens object.

In the formation known as Einstein's Cross four images of the same distant quasar appears around a foreground galaxy due to strong gravitational lensing

There are three classes of gravitational lensing:

1. Strong lensing: where there are easily visible distortions such as the formation of Einstein rings, arcs, and multiple images. The Einstein Cross or Q2237+030 or QSO 2237+0305 is a gravitationally lensed Quasar that sits directly behind ZW 2237+030 Huchra's In observational Astronomy an Einstein ring is the deformation of the light from a source (such as a Galaxy or Star) into a ring through Gravitational
2. Weak lensing: where the distortions of background sources are much smaller and can only be detected by analyzing large numbers of sources to find coherent distortions of only a few percent. While the presence of any mass bends the path of light passing near it this effect rarely produces the giant arcs and multiple images associated with strong gravitational lensing. The lensing shows up statistically as a preferred stretching of the background objects perpendicular to the direction to the center of the lens.
3. Microlensing: where no distortion in shape can be seen but the amount of light received from a background object changes in time. Gravitational microlensing is an astronomical phenomenon due to the Gravitational lens effect The background source and the lens may be stars in the Milky Way in one typical case, and stars in a remote galaxy and an even more distant quasar in another case. The Milky Way (a translation of the Latin Via Lactea, in turn derived from the Greek Γαλαξίας (Galaxias sometimes referred to simply A quasar (contraction of QUASi-stellAR radio source) is an extremely powerful and distant Active galactic nucleus.

The effect is small, such that (in the case of strong lensing) even a galaxy with a mass more than 100 billion times that of the sun will produce multiple images separated by only a few arcseconds. The solar mass is a standard way to express Mass in Astronomy, used to describe the masses of other Stars and galaxies. A minute of arc, arcminute, or MOA is a unit of angular measurement, equal to one sixtieth (1/60 of one degree. Galaxy clusters can produce separations of several arcminutes. Galaxy groups and clusters are the largest Gravitationally bound objects to have arisen thus far in the process of cosmic structure formation In both cases the galaxies and sources are quite distant, many hundreds of megaparsecs away from our Galaxy. History The first direct measurements of an object at interstellar distances were undertaken by German Astronomer Friedrich Wilhelm Bessel in 1838

Gravitational lenses act equally on all kinds of electromagnetic radiation, not just visible light. Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. Weak lensing effects are being studied for the cosmic microwave background as well as galaxy surveys. In Astronomy, a redshift survey, or galaxy survey, is a survey of a section of the sky to measure the Redshift of astronomical objects Strong lenses have been observed in radio and x-ray regimes as well. Radio is the transmission of signals by Modulation of electromagnetic waves with frequencies below those of visible Light. X-radiation (composed of X-rays) is a form of Electromagnetic radiation. If a strong lens produces multiple images, there will be a relative time delay between two paths: that is, in one image the lensed object will be observed before the other image.

Simulation

Simulated gravitational lensing (black hole going past a background galaxy).

To the right is a simulation of gravitational lensing caused by a Schwartzschild black hole passing in front of a background galaxy. In Einstein's theory of General relativity, the Schwarzschild solution (or the Schwarzschild vacuum) describes the Gravitational field outside A secondary image of the galaxy can be seen within the black hole's Einstein radius on the side opposite the galaxy. The Einstein radius is the radius of an Einstein ring, and is a characteristic angle for Gravitational lensing in general as typical distances between images in gravitational The secondary image grows (remaining within the Einstein ring) as the primary image approaches the black hole. The surface brightness of the two images remains constant, but their angular sizes vary, hence producing an amplification of the galaxy luminosity as seen by a distant observer. Surface brightness is a concept used in Astronomy when describing extended Astronomical objects such as galaxies and Nebulae General The angular diameter of an object as seen from a given position is the "visual diameter" of the object measured as an angle Maximum amplification occurs when the galaxy (or in this case a bright part of it) is exactly behind the black hole.

History

According to general relativity, mass "warps" space-time to create gravitational fields and therefore bend light as a result. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS A gravitational field is a model used within Physics to explain how gravity exists in the universe Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 This theory was confirmed in 1919 during a solar eclipse, when Arthur Eddington observed the light from stars passing close to the sun was slightly bent, so that stars appeared slightly out of position. Year 1919 ( MCMXIX) was a Common year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Common A solar eclipse occurs when the Moon passes between the Sun and the Earth so that the Sun is wholly or partially obscured Sir Arthur Stanley Eddington, OM (28 December 1882 – 22 November 1944 was an English Astrophysicist of the early 20th century A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth The Sun (Sol is the Star at the center of the Solar System.

Einstein realized that it was also possible for astronomical objects to bend light, and that under the correct conditions, one would observe multiple images of a single source, called a gravitational lens or sometimes a gravitational mirage. s are significant physical entities, associations or structures which current Science has confirmed to exist in Space. A gravitational mirage is the visual impression caused by a so-called Gravitational lens in space which may include multiple images rings etc of background light sources However, as he only considered gravitational lensing by single stars, he concluded that the phenomenon would most likely remain unobserved for the foreseeable future. In 1937, Fritz Zwicky first considered the case where a galaxy could act as a source, something that according to his calculations should be well within the reach of observations. Fritz Zwicky ( February 14 1898 &ndash February 8 1974) was an American-based Swiss Astronomer of Bulgarian origin A galaxy is a massive gravitationally bound system consisting of Stars an Interstellar medium of gas and dust, and Dark matter

It was not until 1979 that the first gravitational lens would be discovered. It became known as the "Twin Quasar" since it initially looked like two identical quasars; it is officially named Q0957+561. The Twin Quasar (Double Quasar or Old Faithful is also known as Q0957+561, or QSO 0957+561. This gravitational lens was discovered accidentally by Dennis Walsh, Bob Carswell, and Ray Weymann using the Kitt Peak National Observatory 2. Dennis Walsh ( 12 June 1933 &ndash 1 June 2005) was an English Astronomer, born into a poor family in Manchester The Kitt Peak National Observatory ( KPNO) is a United States astronomical Observatory located on a 2096 m (6880 ft peak of the 1 meter telescope. A telescope is an instrument designed for the observation of remote objects and the collection of Electromagnetic radiation.

In the 1980s, astronomers realized that the combination of CCD imagers and computers would allow the brightness of millions of stars to be measured each night. In a dense field, such as the galactic center or the Magellanic clouds, many microlensing events per year could potentially be found. This lead to efforts such as Optical Gravitational Lensing Experiment, or OGLE, that have characterized hundreds of such events. The Optical Gravitational Lensing Experiment is a Polish astronomical project based at Warsaw University that is chiefly concerned with discovering

Explanation in terms of space-time curvature

In general relativity, gravity is not construed as a force; hence, if the net force of non-gravitational interactions is negligible, the law that describes motion is Newton's First Law rather than Newton's Second Law. The Kepler problem in general relativity involves solving for the motion of two spherical bodies interacting with one another by Gravitation, as described by the theory of Newton's laws of motion are three Physical laws which provide relationships between the Forces acting on a body and the motion of the Newton's laws of motion are three Physical laws which provide relationships between the Forces acting on a body and the motion of the Newton's First Law models position as a function of time in non-relativistic mechanics, but in general relativity the law is rewritten to demand motion along a space-time geodesic. In Mathematics, a geodesic /ˌdʒiəˈdɛsɪk -ˈdisɪk/ -dee-sik is a generalization of the notion of a " straight line " to " curved spaces This curvature of space-time causes the path of even a massless particle like a photon to deviate from the straight lines expected from Euclidean intuition; and, in particular, the path is observed to curve in exactly the same way as the geodesics predicted by general relativity. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena

Since the speed of electromagnetic radiation in a vacuum is invariant in both theories of relativity, lensing changes the direction of the velocity vector but not its magnitude. Weak lensing and micro-lensing in particular cause deflection through an angle

$\theta = \frac{GM}{rc^2}$

toward the mass M at a distance r from the affected radiation, where G is the universal constant of gravitation and c is the speed of light in a vacuum. The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass Some care needs to be taken in defining this distance because gravity is not instantaneous: like light, it propagates at speed c. The path of the gravitational wave and the electromagnetic radiation intersect at specific space-time coordinates, and the lensing is determined by the component of the incident gravitational wave perpendicular to the direction of the electromagnetic radiation's motion.

Applications

Actual gravitational lensing effects as observed by the Hubble Space Telescope in Abell 1689 - Enlarge the image to see the lensing arcs

Studying the background sources

Gravitational lenses can be used as gravitational telescopes, because they concentrate the light from objects seen behind them, making very faint objects appear brighter, larger and therefore more easily studied. Abell 1689 is a stellar object described as being a Galaxy cluster and Gravitational lens in the constellation Virgo. Researchers at Caltech have used the strong gravitational lensing afforded by the Abell 2218 cluster of galaxies to detect the most distant galaxy known (February 15, 2004) through imaging with the Hubble Space Telescope. The California Institute of Technology (commonly referred to as Caltech) is a private, Coeducational research university located in Pasadena Abell 2218 is a cluster of galaxies about 2 billion Light-years away in the Constellation Draco. Events 590 - Khosrau II is crowned as king of Persia 1637 - Ferdinand III becomes Holy Roman Emperor "MMIV" redirects here For the Modest Mouse album see " Baron von Bullshit Rides Again " The Hubble Space Telescope ( HST; also known colloquially as "the Hubble" or just "Hubble" is a space telescope that was carried into Objects at such distances would not normally be visible, providing information from further back in time than otherwise possible.

Similarly, microlensing events can be used to obtain additional information about the source star. In addition to the greater brightness, limb darkening can be measured during high magnification events[1]. Limb darkening refers to the diminishing of intensity in the image of a star as one moves from the center of the image to the edge or " Limb " of the image If the source star is part of a binary system, the orbital motion of the source can sometimes be measured (called the xallarap effect, by analogy to parallax which is caused by the orbital motion of the Earth). Xallarap is a variation in a gravitational lensing observation caused by the orbital motion of the source Parallax is an apparent displacement or difference of orientation of an object viewed along two different lines of sight and is measured by the angle or semi-angle of inclination between

Studying the foreground lenses

Observations of gravitational lensing can also be inverted to examine the lens itself. An inverse problem is the task that often occurs in many branches of Science and Mathematics where the values of some model parameter(s must be obtained from the Direct measurements of the mass in any astronomical object are rare, and always welcome. While most other astronomical observations are sensitive only to emitted light, theories are generally concerned with the distribution of mass. Comparing mass and light typically involves assumptions about complicated astrophysical processes. Gravitational lensing is particularly useful if the lens is for some reason difficult to see.

Gravitational microlensing can provide information on comparatively small astronomical objects, such as MACHOs within our own galaxy, or extrasolar planets (planets beyond the solar system). Massive astrophysical compact halo object, or MACHO, is a general name for any kind of astronomical body that might explain the apparent presence of Dark An extrasolar planet, or exoplanet, is a Planet beyond the Solar System, orbiting around other Stars As of September 2008 312 Three extrasolar planets have been found in this way, and this technique has the promise of finding Earth-mass planets around sunlike stars within the 21st century. Any Planet is an extremely faint light source compared to its parent Star. The 21st century is the current century of the Christian Era or Common Era in accordance with the Gregorian calendar. The MOA and PLANET collaborations focus on this research. Microlensing Observations in Astrophysics ( MOA) is a collaborative project between researchers in New Zealand and Japan. The Probing Lensing Anomalies NETwork ( PLANET) collaboration coordinates a network of Telescopes to rapidly sample Photometric measurements of the magnification

3D map of the large-scale distribution of dark matter, reconstructed from measurements of weak gravitational lensing with the Hubble Space Telescope.

Strong and weak gravitational lensing of distant galaxies by foreground clusters can probe the amount and distribution of mass, which is dominated by invisible dark matter. Galaxy groups and clusters are the largest Gravitationally bound objects to have arisen thus far in the process of cosmic structure formation In Physics and cosmology, dark matter is hypothetical Matter that does not interact with the electromagnetic force but whose presence can be inferred from Aside from determining how much dark matter they contain, its distribution in these systems depends upon properties including the mass of its (unknown) constituent particles and their collisional cross-section. The number of strong gravitational lenses throughout the sky can also be used to measure values of cosmological parameters such as the mean density of matter in the universe. Presently, the statistics do not place very strong limits on cosmological parameters, partly because the number of strong lenses found is relatively small (fewer than a hundred). Weak gravitational lensing can extend the analysis away from these most massive clusters and, for example, reconstruct the large-scale distribution of mass. This is sensitive to cosmological parameters including the mean density of matter, its clustering properties and the cosmological constant. In Physical cosmology, the cosmological constant (usually denoted by the Greek capital letter Lambda: Λ was proposed by Albert Einstein as a modification

Geometry of the Universe

A purely geometric effect, gravitational lensing can be used to measure the expansion history of the universe (its size as a function of time since the big bang), which is encoded in Hubble's law. Hubble's law is the statement in Physical cosmology that the Redshift in light coming from distant galaxies is proportional to their distance If the mass distribution in a foreground lens is well understood (typically from multiple strong lensing arcs, and possibly weak lensing in the outskirts), two other free parameters can be used to constrain the Hubble constant, or deviations from Hubble's law caused by dark energy. Hubble's law is the statement in Physical cosmology that the Redshift in light coming from distant galaxies is proportional to their distance In Physical cosmology, dark energy is a hypothetical exotic form of Energy that permeates all of space and tends to increase the rate of expansion of the universe In principle, and in both cases, only one gravitational lens for the best possible measurement. The search continues for that perfect lens, with many multiply-imaged arcs.

There will be a time delay (around days or weeks) between multiple images of the same source because of

1. the delay due to the difference in optical path length between the two rays. In Optics, optical path length (OPL is the product of the geometric length of the path light follows through the system and the Index of refraction of the medium
2. the general relativistic Shapiro effect, which describes light rays as taking longer to traverse a region of stronger gravitation, (see: gravity well, gravitational time dilation). The Shapiro time delay effect or gravitational time delay effect is one of the four classic solar system Tests of general relativity. In Physics, a gravity well is the Gravitational potential field around a massive body (a particular kind of Potential well) Gravitational time dilation is the effect of time passing at different rates in regions of different Gravitational potential; the higher the local distortion of Spacetime Because the two rays travel through different parts of the potential well created by the deflector, the clocks carrying the source's signal will differ by a small amount.

If either the amount or the spectrum of light emitted by the background source varies over time, characteristic variations can be seen to occur first in one image and then others.

A gravitational lens magnifies and distorts very distant sources more than those only just behind the lens (and it does not distort those in front of the lens). Indeed, simple geometry can be used to calculate the efficiency of a gravitational lens as a function of the angular diameter distance to the source. The angular diameter distance is a distance measure used in Astronomy. If the distortion can be measured at multiple distances, this distance can be compared to the redshift of those sources: a direct Hubble diagram. In Physics and Astronomy, redshift occurs when Electromagnetic radiation – usually Visible light – emitted or reflected by Hubble's law is the statement in Physical cosmology that the Redshift in light coming from distant galaxies is proportional to their distance Furthermore, this technique effectively requires only the ratio of the distortion at two distances. The total mass of the foreground lens therefore cancels out and does not need to be constrained (although its radial profile does). Using a more massive lens simply increases the signal to noise of the measurement.

Search for Gravitational lenses

Most of the gravitational lenses in the past have been discovered accidentally. A search for gravitational lenses in the northern hemisphere (Cosmic Lens All Sky Survey, CLASS), done in radio frequencies using the Very Large Array (VLA) in New Mexico, led to the discovery of 22 new lensing systems, a major milestone in the gravitational lenses history. This has opened a whole new avenue for research ranging from finding very distant objects to finding values for cosmological parameters so we can understand the universe better.

A similar search in the southern hemisphere would be a very good step towards complimenting the northern hemisphere search as well as obtaining other objectives for study. As can be expected, if such a search is done using well calibrated and well parametrized instrument and data, we can expect to have a very good outcome. The use of the Australia Telescope 20GHz (AT20G) Survey data collected using the Australia Telesope Compact Array (ATCA) stands to be such a collection of data. As the data was collected using the same instrument maintaining a very stringent quality of data we should expect to obtain good results from the search. The AT20G survey is a blind survey at 20 GHz frequency in the radio domain of the electromagnetic spectrum. Due to the high frequency used, the chances finding gravitational lenses increases as the relative number of compact core objects (eg. Quasars) are higher ( Sadler et al. 2006). This is important as the lensing is easier to detect and identify in simple objects compared to objects with complexity in them. This search involves the use of interferometric methods to identify candidates and follow them up at higher resolution to identify them. Full detail of the project is currently under works for publication.

Historical papers and references

• Chwolson, O (1924). In observational Astronomy an Einstein ring is the deformation of the light from a source (such as a Galaxy or Star) into a ring through Gravitational The Einstein Cross or Q2237+030 or QSO 2237+0305 is a gravitationally lensed Quasar that sits directly behind ZW 2237+030 Huchra's The Twin Quasar (Double Quasar or Old Faithful is also known as Q0957+561, or QSO 0957+561. "Über eine mögliche Form fiktiver Doppelsterne". Astronomische Nachrichten 221: 329.
• Einstein, Albert (1936). Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical "Lens-like Action of a Star by the Deviation of Light in the Gravitational Field". Science 84: 506—507.
• Renn, Jürgen; Tilman Sauer and John Stachel (1997). "The Origin of Gravitational Lensing: A Postscript to Einstein's 1936 Science paper". Science 275: 184—186. doi:10.1126/science.275.5297.184. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.

Citations

1. ^ Stellar Atmospheres. MOA collaboration.