By Naresh Dadhich and Ajit Kembhavi
The great English physicist Sir Isaac Newton had famously said, “If I have seen further than others, it is by standing upon the shoulders of giants.” This is true in general in science. No discovery is made without one standing upon some shoulders, low or high.
Let us look for the possible shoulders Roger Penrose may be standing on, while seeing black-hole formation as the inevitable end-state of a star with a large mass in Albert Einstein’s theory of gravitation, also known as the general theory of relativity. Penrose’s work is in the news currently because it has won him this year’s Nobel prize for physics. He has shared the prize with two other astronomers for their independent work on detecting very large masses that are believed to be a black hole in the centre of our own Milky Way galaxy.
The first Indian connection to the term black hole is an infamous incident in 1756, when the Nawab Siraj-ud-Daulah squeezed 146 British soldiers into a dungeon in Fort William, which got to be known as the Black Hole of Kolkata. (The General Post Office in Kolkata stands on this site at present. No wonder, Kolkata residents complain that no letter comes out of the site!)
It is interesting that the first conception of a black hole as a scientific possibility was to follow pretty soon. In 1784, British clergyman and scientist John Michell and, two years later, the great French mathematician Pierre Simon Laplace argued that if an object is very massive and dense, its gravity can be so strong that even light cannot escape from it. Such an object, if it exists, would be all black and invisible — a black hole!
The modern story begins with Subrahmanyan Chandrasekhar who, after his BSc in Madras, left for Cambridge, England, in 1930 for higher studies. On his voyage to Cambridge, he did interesting calculations on white dwarfs. It was believed until then that all stars would end their life by becoming a white dwarf. This is a very enigmatic object, which supports itself against the force of gravity because of the pressure exerted by electrons. In his mathematical investigation of such objects, the young Chandrasekhar combined Albert Einstein’s theory of relativity and the then new theory of quantum mechanics. He made the startling discovery that there is a maximum mass that a white dwarf can have. This is about 1.4 times the mass of our sun. A white dwarf with mass greater than this value, now called the Chandrasekhar limit, must necessarily collapse. This was a very major discovery. It is a different matter that Sir Arthur Eddington, arguably the most influential and creative astrophysicist of the day, did not accept Chandrasekhar’s monumental discovery and criticised it in a rather unscientific manner. The latter had the last laugh when he was awarded the Nobel prize for his work on white dwarfs in 1983.
What happens when a star cannot end its life as white dwarf because it is too massive? It turns out that as a star continues its collapse, it eventually becomes so dense that almost all matter in it is converted into nuclear particles called neutrons. These neutrons can, like the electrons in white dwarfs, exert pressure to counter the collapse, leading to the formation of a stable object called a neutron star. Such an object is so dense that just a spoonful of its matter would weigh the same as all of humanity. Even such an object has a limiting mass of about three times the mass of the Sun.
If a neutron star is more massive than this limit, it must collapse indefinitely as there is no source of pressure available in the present theory to resist it. It collapses right down to zero size and infinitely large density — a singularity. Even before the object reaches this stage, it becomes so compact that light can no longer escape from it — a black hole is formed! This result is based on Einstein’s theory of general relativity in which gravity and spacetime geometry are beautifully synthesised. Gravity is described by spacetime curvature. That is why black holes in general relativity are more profound and bizarre objects than the black holes in Newton’s theory of gravity described by Michell and Laplace.
The mathematics for such a collapse was first worked out by Bishveshwar Datt of Kolkata in 1938. However, soon after obtaining the important result, he died on the operation table while being operated for hernia. A year later, Robert Oppenheimer (who is known as the father of the first atomic bomb) and David Snyder in the USA obtained the same result as Datt did, which is famously known as the Oppenheimer-Snyder collapse.
Those were the Second World War years, which had made the flow of information from India to abroad difficult. Due to this reason, and the sad and untimely demise of Datt, his contribution remained unsung until 1999, when the Journal of General Relativity and Gravitation discovered him and reprinted the original paper. In all fairness, the result laying the foundation for black hole formation should be termed as Datt-Oppenheimer-Snyder (DOS) collapse.
In 1953, Amal Kumar Raychaudhuri, a lecturer in Ashutosh College, Kolkata, obtained a remarkable equation, which bears his name. This governs the evolution of a system of particles according to Einstein’s theory of gravitation. It is the Raychaudhuri equation that establishes in all generality the profound result that the occurrence of a singularity is inevitable in general relativity. The earlier work of Datt, Oppenheimer and Snyder had made simplifying assumptions which were not used by Raychaudhuri in his seminal work.
In the mid-1960s, Stephen Hawking and Roger Penrose, building on the Raychaudhuri’s equation and employing global analysis techniques made the profound prediction that formation of black hole with a singularity at its centre is inevitable in Einstein’s theory of gravity. They proved very powerful theorems establishing the result mathematically and rigorously. It is this important work which is responsible for the Nobel to Penrose. Hawking could not be included in the prize since it is not awarded to deceased persons.
Though the Raychaudhuri equation leads to the conclusion that singularity is inevitable in gravitational collapse in general relativity, what the powerful theorems of Hawking and Penrose have shown by using the global analysis techniques is that as the collapse proceeds, trapped surfaces would be formed from which matter cannot escape. In essence, the theorems explain the process of black-hole formation in terms of spacetime geometry. Black hole is bizarre and exotic simply because it is purely a geometric object.
The order of profoundness in physics proceeds as follows. At the top is the discovery of a new law of physics. Then come the equations that govern the behaviour of various physical systems, like collapsing stars or the expanding universe. And, finally, we have various important, useful and interesting results which follow from the equations. Einstein’s theory of gravitation led to the many profound results on black holes, the expanding universe and so forth. The role of Raychaudhuri’s equation is clear in this hierarchy.
In 1966, Fred Hoyle and Jayant Narlikar asked the following question: How massive should a star be so as to arrest the cosmic expansion of the surrounding matter and form a galaxy-like structure? They found that it has to have about a billion times the mass of the sun. Thus, they argued that the centre of a galaxy like ours should harbour a supermassive star. The two observers, Andrea Ghez and Reinhard Genzel, have shared the Nobel prize with Penrose for finding a supermassive object (that’s what the citation says) at the centre of our galaxy. It is widely believed that this object is a black hole. It is interesting that what Hoyle and Narlikar had predicted over half a century ago has now actually been observed.
The 1960-70s were highly charged times for great discoveries in relativistic astrophysics and cosmology. Though the solution describing a black hole was obtained immediately after Einstein discovered his equation, it was not understood as a black hole until the 1960s, a good 45 years later. It may be noted that the term black hole was coined by John Wheeler only in 1967, while responding to an audience question in a conference in New York.
The most interesting solution of Einstein’s equations describing a rotating black hole was discovered in 1963 by the New Zealand physicist, Roy Kerr. Another momentous discovery was of the cosmic microwave background radiation at temperature of 2.7 Kelvin (about -270 degrees Centigrade), which was the greatest prediction of the big-bang theory of the universe. The universe had a singular beginning in a hot big-bang, and the observed microwave radiation is carrying that message and signature.
The stage was thus set for the great discovery and prediction that formation of black hole and consequently the central singularity are inevitable features of Einstein’s gravity–general relativity.
Naresh Dadhich is a theoretical physicist, formerly with the Inter-University Centre for Astronomy and Astrophysics (IUCAA) at Pune. Ajit Kembhavi is an astrophysicist at IUCAA
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