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How gravitational lensing was experimentally proved and what is are its major applications at present?
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Where Rμν is the Ricci curvature tensor, gμν is the metric tensor, Tμν is the stress-energy tensor, Λ is the cosmological constant, G is Newton’s gravitational constant and c is the speed of light in vacuum. A tensor is a geometrical representation of a curved four-dimensional curved space-time, and the laws of physics must be expressed in a way that is are valid independently to the coordinate system used to describe points in any space-time where inertial reference frames exist. To solve particular problems a metric should be calculated, and to demonstrate that a massive object alters the light’s trajectory, the Schwarzschild metric is used (space-time geometry outside a stationary spherical distribution of matter), with it the Einstein’s field equations are expressed as:
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Previous to this prediction, Einstein had showed Eddington that his relativity worked to explain the precession of the perihelion of Mercury, precession that Newton’s mechanics failed to explain, but at the time scientists were skeptical about his proposal, as they found Newton not only valid but simple to understand, and the sole prediction of the precession wasn’t enough for them to replace Newton. For that, Eddington devised a way to experimentally prove that relativity was valid, taking advantage of the coming solar eclipse in 1919 and the pass of the Sun in front of the Hyades cluster, the idea was that when the Moon completely covered the Sun, the light from the stars that were behind the Sun would be visible thus a photograph photography of them could be taken, and later compared with an actual photography of the cluster to measure the deflection angle and compare it with Einstein’s predictions.
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where β is the ring’s angle, dL is the angular diameter to the lens, dS is the angular diameter distance to the light source and dLS is the angular diameter distance between the lens and the light source; the possibility to actually detect those lenses comes from the angular resolving of the instruments used by astronomers compared to this angle.
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One of the applications of this phenomenon is the detection of black holes, as their name suggests, a black hole cannot be directly seen because there is no light coming from them, for that reason at first they could only be detected due to the gravitational lensing created by their massive nature, the following figure shows a simulation of a black hole’s gravitational lensing:
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