Gravitational lensing, one of the feel-good and amazing concepts in Physics. Just like an optical lens, a high gravitational field distorts the direction of light. It is somewhat similar to an electron microscope, where the electromagnetic force distorts electron beams in a controlled manner. Here, gravity does it, but not in a controlled manner. This idea actually arose when Newtonian Mechanics dominated the field of Physics, and the refined, impactful, and clear version of this came as a result of Einstein’s General Relativity. Let’s explore gravitational distortion of light.

On May 29, 1919, Arthur Eddington, Frank Watson Dyson, and their team were waiting for the precious moment to observe the stars near the Sun. The Moon completely blocked the Sun — a total solar eclipse. They were the first to witness the deflection of light by a high-mass object’s gravity. This observation was made simultaneously in Sobral city, Brazil, and São Tomé and Príncipe on the west coast of Africa. This was the first clear proof of General Relativity and made relativity and Albert Einstein famous.

“I would feel sorry for the dear Lord. The theory is correct anyway.”

Said by Einstein when one of his assistants asked what his reaction would have been if General Relativity had not been confirmed by Eddington and Dyson.

In 1784, Henry Cavendish suggested that light might be affected by gravity, and in 1801, Johann Georg von Soldner showed that Newtonian gravity predicted that light would bend around massive objects. Einstein’s deflection of light value calculated only using the Equivalence Principle is the same as Soldner’s value of light deflection. The calculations based on Newtonian mechanics are as follows,

Newtonian Gravitational Light Distortion

Under Newtonian gravity, treat light as a particle of mass $m$ moving with velocity c past a mass $M$ with impact parameter $b$.

The gravitational force is

The transverse acceleration is

For a nearly straight trajectory,

The transverse velocity change is

Using $dt = \frac{dx}{c}$,

The integral evaluates to

Thus,

The deflection angle (for small angles) is

This is the Newtonian prediction.

Calculations of Einstein using the Equivalence Principle

Using the Equivalence Principle, consider a light beam passing a mass $M$. In a uniformly accelerated frame with acceleration $g$, light bends because during time $t$, the vertical displacement is

For a light ray passing near the surface of a mass M,

The time spent near the mass is roughly

Thus,

The deflection angle is approximately

This matches the Newtonian result.

Gravitational Lensing from the Perspective of General Relativity

In General Relativity, gravity is not a force but curvature of spacetime. The spacetime around a spherical mass $M$ is described by the Schwarzschild metric:

Light follows null geodesics $(ds^2 = 0)$. Solving the geodesic equation for a photon trajectory in the weak-field approximation gives the total deflection angle

This is exactly twice the Newtonian (or Equivalence Principle) value.

For light grazing the Sun,

which matches the 1919 eclipse observations.

History of Theory

In 1924, the Soviet physicist Orest Khvolson, who lived in St. Petersburg, noted gravitational lensing and discussed it in print. Also in 1936, František Link worked on it. The idea of gravitational lensing is commonly associated with Einstein, who made unpublished calculations on it in 1912.

Unlike other optical lenses, a point-like gravitational lens gives maximum deflection near its center and the lowest deflection at points far from the center. So it has a focal line, while an optical lens has a single focal point. If the light source, a massive more spherical lensing object, and the observer lie in a straight line, then a ring-like image of the light source appears around the lensing object. This phenomenon was first mentioned by Orest Khvolson and later quantified by Einstein in 1936. It is more familiarly known as the Einstein Ring (Einstein–Khvolson Ring). If the lensing mass is complex or if there is misalignment, the observer will see arc segments or multiple images. If the alignment is good and the lensing object is more elliptical, we get four images on each side of the lensing object. That phenomenon is known as the Einstein Cross.

In November 2015, scientists predicted a supernova using gravitational lensing because they had already seen multiple images of a supernova whose light was lensed by the uneven galaxy cluster MACS J1149.5+2223.

Strong Gravitational Lensing

Consider that you are standing on a planet and in the sky you see an Einstein ring, arc, or Einstein Cross — you are witnessing strong gravitational lensing. This means the lensing object is denser than the critical surface mass density. The formula for the critical surface mass density is

where $D_S$ is the distance to the source, $D_L$ is the distance to the lens, and $D_{LS}$ is the distance between the source and the lens.

Weak Gravitational Lensing

Weak gravitational lensing is the method of analysing the distribution of mass in space. If mass is present, light bends and forms small distortions. This rarely produces arcs or multiple images, and it is very hard to analyse with a single light source. The effects of cluster strong lensing were first detected by Roger Lynds of the National Optical Astronomy Observatories and Vahe Petrosian of Stanford University, who discovered giant luminous arcs in a survey of galaxy clusters in the late 1970s. Lynds and Petrosian published their findings in 1986 without knowing the origin of the arcs. In 1987, Geneviève Soucail of the Toulouse Observatory and her collaborators presented data of a blue ring-like structure in Abell 370 and proposed a gravitational lensing interpretation. The first cluster weak lensing analysis was conducted in 1990 by J. Anthony Tyson of Bell Laboratories and collaborators. Tyson et al. detected a coherent alignment of the ellipticities of faint blue galaxies behind both Abell 1689 and CL 1409+524.

Micro Gravitational Lensing

Microlensing is the phenomenon used to identify objects from the mass of planets to stars, regardless of the light emitted by the object. When a distant star or quasar becomes sufficiently aligned with a massive compact foreground object, the bending of light due to its gravitational field results in observable magnification. The time scale of the transient brightening depends on the mass of the foreground object as well as on the relative proper motion between the background “source” and the foreground “lens” object.

Ideally aligned microlensing produces a clear separation between the radiation from the lens and source objects. It magnifies the distant source, revealing it or enhancing its size and brightness. It enables the study of faint or dark objects such as brown dwarfs, red dwarfs, planets, white dwarfs, neutron stars, black holes, and massive compact halo objects.

These are the pieces of information I gathered from my exploration. It makes me wonder — cosmology is really a great field to explore. I will explore more. Stay connected with Formulon for more explorations.

Read our Article Discuss Dark Energy Understanding Dark Energy: The Universe’s Greatest Mystery

Reference

• Gravitational Lens -Wikipedia
• Gravitational Lensing – CFA- Harvard
• Beginner’s Guide to Gravitational lens – BBC Sky at Night Magazine