What is gravitational lensing all about?

Gravitational lensing is a phenomenon by which light rays are bent by gravitational sources (i.e big masses) due to General Relativity.

NASA, ESA, and A. Feild (STScI)

Gravitational lensing can be classed into several types based on the amount of distortion seen in the image:

1. Strong: Multiple images or large arcs are produced
2. Weak: Arclets and some shearing are seen
3. Microlensing: Brightness varies over time due to relative movement of multiple bodies (e.g., an orbiting exoplanet)

Why does gravity bend light? This is because gravity causes curvatures in the fabric of spacetime, and light rays follow the curvature of space and bend along with spacetime. In technical terms, we say that light rays follow null geodesics, or maximum-length casual curves. But the end result is that gravitational lensing can look a lot like optical lensing that happens in ordinary magnifying glasses, telescope lenses, etc. (a key difference is that optical lenses can show chromatic aberration where light of different wavelengths are bent by differing amounts, while this does not happen in gravitational lensing).

The main kinds of optical phenomena by which we recognize cosmic gravitational lenses include: Multiple Images, Einstein Rings, Magnification, and Shear.

1. http://www.spacetelescope.org/static/archives/images/screen/potw1204a.jpg
2. Claeskens et al., 2006. Multi wavelength study of the gravitational lens system RXS J1131-1231.
3. http://apod.nasa.gov/apod/ap090921.html

Why is gravitational lensing so important? For one, lensing can act as a natural telescope and focus and magnify light. This allows us to detect very distant or small cosmic objects such as galaxies or exoplanets that would otherwise be invisible to our telescopes. Another very important reason is the detection of  dark matter. Normally dark matter cannot be seen, but its mass exerts gravity that in turn, bends light. See the Bullet Cluster for a striking example (Clowe, D., and et al., 2006. A Direct Empirical Proof of the Existence of Dark Matter).

Normally, light rays curved by gravity are really curved and are represented by solutions to second-order ordinary differential equations (ODEs) which are expensive to solve. See for example the black dashed and solid curves in the figure below from this article: http://arxiv.org/abs/1302.4369v2

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