The region around the supermassive black hole at the centre of the Milky Way, imaged with South Africa’s MeerKAT radio telescope. Credit: South African Radio Astronomy Observatory (SARAO).
This year’s Nobel Prize in physics was shared between mathematical physicist Roger Penrose and astronomers Reinhard Genzel and Andrea Ghez – for their contributions to the study of black holes. While Penrose was honoured “for the discovery that black hole formation is a robust prediction of the general theory of relativity,” Genzel and Ghez were recognised “for the discovery of a supermassive compact object at the centre of our galaxy.”
Black holes are perhaps the most enigmatic objects in the Universe. A black hole harbours a singularity at its centre, where all known physical laws break down. This singularity is clothed by an event horizon – an imaginary surface that prevents anything, including light, from escaping it.
Albert Einstein’s general theory of relativity admits the existence of such objects, and Karl Schwarzchild first discovered this possibility in 1915. However, even Einstein didn’t believe that such objects could exist in the natural world. Even when theoretical evidence suggested that black holes could be formed by the gravitational collapse of massive stars, many leading physicists did not agree. Arthur Eddington expected that “there should be a law of nature to prevent the star from behaving in this absurd way.”
Although during the first half of the 20th century black holes were restricted to the domain of mathematical studies, recent astronomical observations suggest that the universe is littered with black holes. Astronomers believe that our own galaxy hosts a supermassive black hole at its centre (which is a few million times more massive than the Sun) – apart from 100 million “small” black holes, each several times more massive than the Sun. And our galaxy is just one among 100 billion galaxies in the observable universe!
Discovering black holes in general relativity
Soon after Einstein published his theory of general relativity, hints started coming out that the theory predicted rather unusual features of the gravitational field. Subrahmanyan Chandrashekhar showed that a star, specifically a white dwarf, with a mass larger than a certain value – known as the Chandrashekhar limit – will inevitably collapse under its own gravity. Ultimately, the gravitational field at its centre becomes infinite, producing a singularity in space-time.
Chandrashekhar’s ideas were developed further by J. Robert Oppenheimer and Hartland Snyder. They showed that when the radius of the collapsing star becomes smaller than a characteristic length, even light emitted from the surface of the star will not reach outside observers. Beyond this point, the star collapses into a singularity. (Interestingly, a similar calculation was performed by a mysterious young Indian physicist named B. Datt a year earlier than Oppenheimer and Snyder, and whose work remained largely unnoticed until recently.)
However, Einstein and many other leading physicists doubted the universality of these solutions. The problem was that they assumed some idealised conditions that were not guaranteed to be present in the real world.
Ironically, a month after Einstein’s death, an Indian physicist, Amal Kumar Raychaudhuri, produced from simple geometric identities a remarkable equation showing that a collection of particles moving in a gravitational field produced by matter (that satisfied some physically reasonable conditions) eventually move towards each other and collide. These collision points were a cornerstone for Roger Penrose to develop his own beautiful ideas, which showed the inevitably of singularity in a gravitational collapse.
The work of Penrose involved several remarkable new mathematical techniques that were grounded in simple physical ideas. The foremost among them was the idea of a trapped surface. In the Newtonian theory of gravity, we are familiar with the notion of the escape velocity: it is the minimum velocity required by a body to escape the gravitational field of a planet or a star. As velocities are relative in Einstein’s theory, no sensible notion of escape velocity was known until Penrose defined the concept of a trapped surface.
The basic idea of the trapped surface is rather simple. Imagine we send two families of light rays (which are located along a circle) such that one family is emitted radially outward and the other, radially inward. We would naïvely expect that at any future instant of time, the circle spanned by the outgoing rays to be larger than the circle spanned by the ingoing rays.
However, Penrose showed that in the presence of a gravitational field, both of these circles can be smaller than the circle from which they are emitted. If this happens, the initial circle is called a trapped surface. Using this idea and Raychaudhuri’s equation, Penrose proved a remarkable mathematical theorem showing that, under reasonable physical conditions (which are satisfied in gravitational collapse), the formation of a singularity is inevitable. This effectively showed that black hole formation is a robust prediction of general relativity.
Penrose’s singularity theorem had a multifold impact. It led to later theorems by Penrose and Stephen Hawking, which placed the mathematical theory of black hole formation on a rigorous footing. Hawking also later used Penrose’s ideas to prove the existence of big-bang singularities in cosmological space-times. Penrose’s work on black holes marked the beginning of a new era of general relativity in which sophisticated mathematical techniques were combined with simple physical insights.
Observing black holes
Mathematical physicists like Penrose tried to answer whether black holes could exist in the physical world. Whether black holes do exist in the universe is a different question, which belongs to the domain of observational astronomy.
Since the 1960s, a large body of observational evidence supporting the existence of massive and compact objects has arisen. Early observations include that of extremely luminous objects like quasars, whose brightness can only be explained by invoking gas accreting onto a supermassive compact object, like a black hole. While quasars are practically located at the edges of the visible universe, astronomers have also observed “micro-quasars” in our own galaxy, which are believed to be smaller black holes accreting gas from a neighbouring star.
Among the most convincing evidence for the existence of black holes comes from the observation of stars at the centre of our own galaxy, the Milky Way. This area, located in the Sagittarius constellation, was known to host a bright radio source called Sagittarius A* (Sgr A*), although this is clearly a misnomer. Sgr A* is nothing like a star.
Two teams of astronomers, led by Reinhard Genzel in Europe and Andrea Ghez in the US, started observing the motion of stars around this object from the 1990s. This is a challenging task. First, localising these stars requires telescopes with very high spatial resolution. Second, the optical emission from these stars is obscured by interstellar dust. In order to overcome these difficulties, they relied on near-infrared observations (wavelengths slightly longer than that of optical light) using the world’s most powerful telescopes, further aided by a host of advanced technologies like adaptive optics.
These observations revealed that stars around the galactic centre are moving at incredible speeds – several thousands of kilometres per second. Some of them even completed full orbital revolutions within the observation period of three decades. This is remarkable. For example, our Sun takes about 200 million years to complete one orbit around the galactic centre. The enormous gravitational attraction of the central object is making these stars move at astonishing speeds.
From the orbital motion of these stars, one can easily compute the mass of the object at the centre, just as we can calculate the mass of the Sun from the motion of planets around it. These calculations showed that this unseen object has a mass 4-million times the mass of the Sun. The simplest explanation was that our galactic centre hosts a supermassive black hole.
A variety of observations suggest that most galaxies host supermassive black holes at their centres, each millions to billions of times more massive than the Sun. Recently, an international array of radio telescopes, belonging to the Event Horizon Telescope project, produced the first image of the supermassive black hole in our neighbouring galaxy, Messier 87. A similar image of the Sgr A* black hole is expected soon. Supermassive black holes seem to play a major role in the evolution of galaxies over cosmic time. Still, we are unsure as to how such giants are produced in nature.
X-ray observations have uncovered several stellar-mass black hole candidates in our own galaxy – believed to be the remnants of massive stars that underwent gravitational collapse at the end of their lifetimes. More recently, gravitational-wave observations by LIGO and Virgo have detected many colliding black holes in the distant universe. In addition, there have been some observational hints of intermediate-mass black holes that are a hundred to a thousand times as massive as the Sun. Cosmologists have also speculated the possibility of ‘primordial’ black holes, which could have been produced by the gravitational collapse of highly dense regions in the early universe. Why, some scientists have even argued that the elusive dark matter could be composed of primordial black holes.
Strictly speaking, the astronomical observations described above only suggest the existence of massive and compact objects that are consistent with being black holes. Thus far, we have no “smoking gun” evidence of singularities or event horizons – which are the true hallmarks of black holes.
Astronomical observations, in particular those using gravitational waves, are starting to probe the precise nature of these compact objects. At the same time, theorists are grappling with the problem of singularities, the places where the current physical laws fail. A satisfactory resolution of singularities that requires a quantum theory of gravity would not only mark a new era in the study of black holes but also expand the horizons of our understanding of nature.
Parameswaran Ajith and Alok Laddha are physicists at the International Centre for Theoretical Sciences, Bengaluru, and the Chennai Mathematical Institute, Siruseri.