Gravitational Lensing

Core Idea

Gravitational lensing is the deflection of light by massive objects, a direct consequence of photons following null geodesics in curved spacetime. For a photon passing a mass M with impact parameter b, GR predicts a deflection angle α = 4GM/(bc²), which is twice the naive Newtonian prediction. Strong lensing near galaxies and galaxy clusters produces multiple images, arcs, and Einstein rings; weak lensing produces subtle statistical distortions of background galaxy shapes used to map dark matter. Microlensing (temporary brightening) is used to detect compact objects and exoplanets. The 1919 solar eclipse observation of starlight deflection by the Sun, confirming the factor-of-two GR prediction over the Newtonian value, was the first experimental validation of general relativity.

Explainer

The bending of light by gravity is a direct prediction of general relativity. Photons follow null geodesics — paths with ds² = 0 — in the curved spacetime around a massive object. Even in Newtonian gravity, one could naively calculate a deflection by treating a photon as a particle with mass m moving at speed c in a gravitational potential (Soldner's calculation from 1801 gives α = 2GM/bc²). Einstein initially published this Newtonian value in 1911. But when he completed the full theory in 1915, the correct GR result turned out to be twice as large: α = 4GM/(bc²), where b is the closest approach distance (impact parameter). The extra factor of 2 comes from the spatial curvature (the g_{rr} perturbation), which affects photons equally to the temporal curvature but is negligible for slowly moving particles.

The confirmation came in 1919 when Arthur Eddington led expeditions to observe a total solar eclipse from the island of Principe and from Sobral, Brazil. Stars whose light passed near the Sun's limb appeared displaced outward by about 1.7 arcseconds, consistent with the GR prediction of 1.75 arcseconds and inconsistent with the Newtonian prediction of 0.87 arcseconds. The result made Einstein an international celebrity. Modern measurements using very long baseline interferometry (VLBI) of radio quasars achieve far better precision, confirming the GR deflection to 0.01% accuracy through the Shapiro effect and astrometric measurements.

Gravitational lensing scales from solar-system tests to cosmological structures. Strong lensing occurs when a massive galaxy or galaxy cluster bends light from a more distant source dramatically enough to produce multiple images, arcs, or complete Einstein rings. The angular radius of an Einstein ring is θ_E = √(4GM D_{LS}/(c² D_L D_S)), typically about 1 arcsecond for galaxy-mass lenses. Strong lensing provides mass estimates for the lens and can magnify distant sources, acting as a natural telescope. The first observed gravitational lens was the "Twin Quasar" Q0957+561, discovered in 1979.

Weak lensing operates at larger angular scales where the deflections are too small to produce multiple images but large enough to distort the shapes of background galaxies by a few percent. By measuring the statistical correlation of these shape distortions across thousands of galaxies, astronomers reconstruct the projected mass distribution of the foreground structures. This technique directly maps dark matter, since the lensing signal depends on total mass regardless of whether it emits light. Weak lensing surveys have mapped the cosmic web of dark matter filaments, constrained the total matter density of the universe, and placed competitive bounds on the equation of state of dark energy. Microlensing — the temporary magnification of a background star by a compact foreground object — is sensitive to objects as small as planets and is used to detect exoplanets and constrain the population of compact dark objects in our galaxy.