Einstein ring Formalism Strong lensing Microlensing Weak lensing
Strong lens systems
Abell 1689
Abell 2218 CL0024+17
Bullet Cluster QSO2237+0305
SDSSJ0946+1006 B1359+154
QSO 0957+561
Surveys
Strong: CLASS
SLACS
SDSS
Micro: OGLE
Gaia Weak: DLS
Pan-STARRS
CFHTLS
DES
LSST
SNAP
DESTINY
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For broader coverage of this topic, see Gravitational lens.
In general relativity, a point mass deflects a light ray with impact parameter by an angle approximately equal to
where G is the gravitational constant, M the mass of the deflecting object and c the speed of light. A naive application of Newtonian gravity can yield exactly half this value, where the light ray is assumed as a massed particle and scattered by the gravitational potential well. This approximation is good when is small.
In situations where general relativity can be approximated by linearized gravity, the deflection due to a spatially extended mass can be written simply as a vector sum over point masses. In the continuum limit, this becomes an integral over the density , and if the deflection is small we can approximate the gravitational potential along the deflected trajectory by the potential along the undeflected trajectory, as in the Born approximation in quantum mechanics. The deflection is then
where is the line-of-sight coordinate, and is the vector impact parameter of the actual ray path from the infinitesimal mass located at the coordinates .[1]
^Bartelmann, M.; Schneider, P. (January 2001). "Weak Gravitational Lensing". Physics Reports. 340 (4–5): 291–472. arXiv:astro-ph/9912508. Bibcode:2001PhR...340..291B. doi:10.1016/S0370-1573(00)00082-X. S2CID 119356209.
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