A black hole.

A team of researchers from Khalifa University has used the theory of General Relativity to figure out a new way to detect cosmic strings across the universe. The team applied the concept of ‘gravitational lensing’ to a family of pairs of black holes connected by a cosmic string in what is known as a C-metric, and computed the first ever lensing formula that can be coupled with existing technologies to chart our universe.

Dr. Davide Batic, Associate Professor of Mathematics, Maha Alrais Alawadi, student from the Department of Mathematics, and Dr. Marek Nowakowski, Associate Professor from the Universidad de los Andes, Columbia, published their work last month in the journal Classical and Quantum Gravity.

What is gravitational lensing?

According to Einstein, the presence of a mass deforms the space-time geometry in such a way that light rays passing nearby get deflected. This is the idea behind gravitational lensing, where rays of light bend near sources of gravitation, such as stars. The greater the mass, the greater the gravity and the closer to the source of gravity, the greater the bending. This effect was observed for the first time in 1919, when English physicist Arthur Eddington measured the position of stars near the Sun before a total eclipse of the Sun and during the eclipse. By doing this, Eddington could discern if the Sun’s gravity bent the rays of light from these nearby stars.

The stars did appear to be displaced, but only by a small amount. However, this was compatible with what was predicted by Einstein’s theory of General Relativity. The mass of the Sun had caused the light to bend only at the plasma limb, or the very edge of the Sun.   Khalifa University, Abu Dhabi.

“What Eddington observed was the least striking aspect of this gravitational distortion,” explained Dr. Batic. “However, scientists soon realized that this phenomenon could be used to probe the cosmic depths with an accuracy never imaged before, opening the door to modern cosmology. Gravitational lensing became and still is an extremely active research field.”

Modern technology in astronomy can measure the relative position of the stars, using this technique.

Imagine two stars and the Earth in a line: the effect of gravitational lensing would bend the light from the furthest star around the nearest star, creating a a displaced faint image of the star, which otherwise would be impossible to observe.  If we replace the gravitational source between the Earth and the distant star with a black hole, light rays emanating from the distant star may get caught by the black hole. These rays may move around a circular orbit in the exterior of the black hole and we would observe a ring of light around the black hole. In this way, we could infer the existence of the distant and apparently hidden bright gravitational object. This hypothetical effect is what scientists call an “Einstein ring.” Since the prediction of the light bending rule of general relativity, which suggests a direct interaction between gravitation and electromagnetism, several distorted images of distant galaxies, stars, star clusters and Einstein rings have been detected by extremely sensitive telescopes. The strong evidence of gravitational lensing in the universe suggests that this technique could be used to infer the existence of black holes scattered across the universe.

Using gravitational lensing to spot black holes

Light rays passing very close to a black hole may experience very strong deviations allowing us to ‘see’ black holes whether the light source is behind the black hole (standard gravitational lensing) or in front of the black hole (retrolensing).

“Light bending and possible bound states of light are genuine effects of general relativity,” explained Dr. Batic. “Whereas light bending has been studied and even observed in a variety of situations, bound orbits of massless particles are an interesting phenomenon and they deserve special attention.”

The research team investigated the effects of gravitational lensing on two black holes in a C-metric. A C-metric describes space-time with two black holes; one black hole here in this universe and one in a parallel universe. The two black holes have equal mass and are accelerating away from each other at a constant rate as a ‘cosmic string’ pulls the black holes apart. The team realized that the black holes in a C-metric would scatter light rays in such a way that would allow for gravitational lensing to detect them.

“There are two kinds of gravitational lensing: weak and strong lensing,” explained Dr. Batic. “Weak lensing occurs when the light rays emanating from the source pass at a distance from the gravitational object in the middle. Strong lensing occurs when the light rays travel very close to the gravitational source, and particularly when close to a special distance from the object called the photon sphere.”

While weak lensing for two uncharged black holes connected by a cosmic string is too small to be detected, strong lensing would indeed work, and the team went on to calculate the formula for detecting black holes in this way.

Their computations found that a weak lensing analysis applied to a supermassive black hole or anything smaller cannot discriminate what kind of metric is being represented. However, their new equations represent the general formula for using black holes in strong gravitational lensing and can be used with observational data to confirm or disprove the existence of black holes described by a C-metric.

“In order to understand the relevance of our result, we need to remember that in theoretical physics, String Theory or the Theory of Everything is our best candidate theory which brings together quantum mechanics with general relativity,” explained Dr. Batic. “Among several predictions provided by String Theory, we also find the so-called cosmic strings. If cosmic strings are observed by means of our theoretical predictions, this would provide the first experimental evidence of a string theory model underlying the structure of spacetime.”