The sense of relief didn’t last long. In 1930, during an 18-day voyage from Madras to work with Eddington and Fowler in Cambridge, a 19-year-old physicist named Subrahmanyan Chandrasekhar decided to calculate just how powerful electron degeneracy pressure could be. Fowler had not placed an upper limit on the mass of a star supported in this way, and it seems most physicists assumed there should be none. But Chandrasekhar realised that electron degeneracy pressure has its limits. Einstein’s theory of relativity says that no matter how confined an electron becomes, the speed of its jiggles cannot exceed the speed of light. Chandrasekhar calculated that the speed limit will be reached for a white dwarf with a mass around 90 per cent that of the Sun.5 A more accurate calculation reveals that the Chandrasekhar limit, as it is now known, is 1.4 times the mass of the Sun. If a collapsing star exceeds this mass, the electrons no longer provide enough pressure to resist the inward pull of gravity because they are moving as fast as they can, and gravitational collapse must continue. Eddington was unimpressed. He felt that Chandrasekhar had incorrectly meshed relativity with the then-new field of quantum mechanics and, when done correctly, the calculation would show that white dwarf stars could exist up to arbitrarily large masses. The subsequent argument between the young Chandrasekhar and the venerable Eddington affected Chandrasekhar deeply. Decades after Eddington’s death in 1944, Chandrasekhar still described this time as ‘a very discouraging experience … to have my work completely discredited by the astronomical community’. Chandrasekhar was ultimately proved correct, and he received the Nobel Prize for his work on the structure of stars in 1983.
Chandrasekhar’s result, published in 1931, was not regarded as definitive evidence that black holes must form. Einstein was still concerned about the apparent freezing of time on the event horizon in 1939. Perhaps there is some other process that can provide support for a collapsing white dwarf when electron degeneracy pressure fails? In the late 1930s, the American physicist Fritz Zwicky and the Russian physicist Lev Landau suggested, correctly, that there may be even denser stars than white dwarfs that are supported not by electron degeneracy pressure but by neutron degeneracy pressure. Under the extreme conditions found in gravitational collapse, electrons can be forced to fuse together with protons to form neutrons and lightweight particles called neutrinos, which escape the star. Neutrons, just like electrons, jiggle around as they are squashed close together, but because they are more massive than electrons, they can provide more support. These objects are neutron stars.
It’s not unreasonable to wonder whether this fate might be the end of the road for all supermassive stars, even though the experience with white dwarfs suggests that neutron degeneracy pressure should also have its limits. Maybe the most massive stars eject material into space as they collapse, or maybe they bounce and explode as they reach neutron star densities. These possibilities were not easily dismissed at the time – nuclear physics was a very new field and the neutron itself was only discovered in 1932.
By 1939, J. Robert Oppenheimer and his student George Volkov, building on work by Richard Tolman, had established what is now called the Tolman–Oppenheimer–Volkov limit, which places an upper limit on the mass of a neutron star at just under three times the mass of the Sun. Oppenheimer and another of his students, Hartland Snyder, subsequently showed that, under certain assumptions, the heaviest stars must collapse behind an event horizon to form a black hole.6 This landmark paper begins: ‘When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star’s mass to the order of that of the Sun, this contraction will continue indefinitely.’ The final lines of the introduction detail the consequences for the flow of time at the horizon that so worried Einstein: ‘The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.’§ In other words, it takes around a day for a star not very much bigger than the Sun to collapse out of existence from the point of view of someone riding inwards on the surface of the collapsing star, but an eternity for anyone watching from the outside. This is the puzzling behaviour of time we noted previously. Oppenheimer and Snyder accepted this basic result of general relativity and showed that it leads to no contradiction. We will explore these intriguing results in more detail in the following chapters.
At this point, World War II intervened, and the thoughts of the world’s physicists turned to supporting the war effort. In the United States, the expertise in nuclear physics honed by the study of stars was particularly relevant to the development of the atomic bomb, and Oppenheimer famously became the scientific leader of the Manhattan Project. When the war ended and the physicists returned, a new generation was poised to take up the mantle. In the United States, that generation was nurtured by John Archibald Wheeler. It was Wheeler who first coined the term black hole at a lecture in the West Ballroom of the New York Hilton on 29 December 1967. In his autobiography, Wheeler describes his intellectual struggles with black holes throughout the 1950s.7 ‘For some years this idea of collapse to what we now call a black hole went against my grain. I just didn’t like it. I tried my hardest to find a way out, to avoid compulsory implosion of great masses.’ He recounts how he eventually became convinced that ‘nothing can prevent a large-enough chunk of cold matter from collapsing to a dimension smaller than the Schwarzschild radius’. Wheeler’s intellectual conversion culminated in a 1962 paper with his student Robert Fuller in which they conclude that ‘there exist points in spacetime from which light signals can never be received, no matter how long one waits’.8 These are the points inside the event horizon from which the Universe beyond is forever isolated. Black holes, it seems, are unavoidable. Any remaining theoretical concerns were dispelled in 1965 by Sir Roger Penrose’s Nobel Prize-winning paper ‘Gravitational Collapse and Space-Time Singularities’, a three-page tour-de-force in which Penrose proves that, in Wheeler’s words, ‘for just about any description of matter that anyone has imagined, a singularity must sit at the centre of a black hole’.9
A profound glow
Our brief history of black holes brings us to 1974 and a paper by Stephen Hawking, which led to an apparently simple question that has driven black hole research for half a century since its publication.
By the 1970s the existence of black holes was widely accepted by theorists, although they were yet to be sighted by astronomers, and the attention of the small group still interested in them turned to the conceptual challenges they pose. Hawking’s paper, published in the journal Nature, is colourfully titled ‘Black Hole Explosions?’10 Hawking showed that the presence of an event horizon has a dramatic effect on the vacuum of space in its vicinity. Quantum theory tells us that empty space is not empty. It is filled with fields that are constantly fluctuating, and these fluctuations manifest themselves as the potential to create particles: photons, electrons, quarks, any particles, in fact. The vacuum has a structure. In common or garden empty space, these fluctuations come and go; one might picture so-called virtual particles continually popping into and out of existence, but the net result is that no real particles ever appear miraculously out of nothing. The presence of the horizon disrupts this balance, with the result that the fleeting virtual particles can become real. These particles, known as Hawking radiation, stream out into the Universe carrying a tiny fraction of the black hole’s energy with them. Over unimaginable time scales, vastly longer than the current age of the Universe, a typical black hole will evaporate away and, ultimately, explode. Black holes, to use Hawking’s famous phrase, ain’t so black. They glow gently like faint coals in the cold sky. Very faint coals. The temperature of a solar mass black hole is 0.00000006 degrees Celsius above absolute zero, which is far colder than the Universe today.¶ Sagittarius A* is even colder: 4.31 million times colder to be precise. But the temperature of a black hole is not zero, and that matters enormously. It means, as we’ll discover, that black holes obey the laws of thermodynamics – the same laws that govern glowing coals and steam engines and stars – and it means they are not immortal. One day in the far, far future, they will all be gone.