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(Image: Richard Kail/SPL)

IT WAS while serving in the German army on the Russian front that, in the winter of 1915-1916, the physicist Karl Schwarzschild sent Albert Einstein some papers. He had solved Einstein’s equations of general relativity for the first time, and shown what happens to space-time inside and outside a massive object – in this case, a perfectly spherical, non-spinning star. Einstein was thrilled.

He wouldn’t be so thrilled with a prediction that eventually emerged from Schwarzschild’s work. Make a star compact enough and it could develop a gravitational pull so great, and warp space-time so much, that even light would not escape.

Just months after his exchange with Einstein, Schwarzschild was dead. It was left to others to work through the details of these curious compact objects, the surfaces of which became known as Schwarzschild singularities.

Chief among them was a young Indian physicist named Subrahmanyan Chandrasekhar. In 1930 he boarded a steamer from India to the UK, where he was to take up a scholarship at the University of Cambridge. Whiling away the 18-day voyage, he worked on the properties of highly compact white-dwarf stars. He found that if they had more than 1.4 times the sun’s mass, they would implode under their own gravity, forming a Schwarzschild singularity.

This did not go down well. At a meeting of the Royal Astronomical Society in 1935, the eminent astrophysicist Arthur Eddington declared that “there should be a law of nature to prevent a star from behaving in this absurd way”. In 1939, Einstein himself published a paper to explain why Schwarzschild singularities could not exist outside the minds of theorists.

The impasse remained until the 1960s, when physicists such as Roger Penrose proved that black holes – a term coined at about this time, probably by astrophysicist John Archibald Wheeler – were a seemingly inevitable consequence of the collapse of massive stars. At a black hole, physical quantities such as the curvature of space-time would become infinite, and the equations of general relativity would break down.

Not only that, but a black hole’s interior would be permanently hidden behind its event horizon, the surface of no return for light. That in turn meant that nothing happening in the interior could influence events outside, because no matter or energy could escape. “The first major paradigm shift was the understanding that these solutions [of general relativity] are meaningful, and that there is a notion called a horizon, and that it is a causal barrier separating the inside from the outside,” says theorist of the University of California, Santa Barbara (UCSB).

Although we can’t see a black hole directly, in 1970 astronomers observing a compact object in the constellation Cygnus saw jets of X-rays consistent with theoretical predictions of radiation streaming from hot matter spiralling towards an event horizon. Since then, our appreciation of black holes’ reality has only grown. It seems most galaxies, including our Milky Way, have a supermassive example lurking at their heart (see “How I’m going to photograph a black hole“).

Yet the ins and outs of black holes remain hotly disputed – not least for what they say about general relativity’s failure to mesh with quantum theory (see “General relativity at 100: Still no theory of everything“). “You have to go to pretty extreme environments for both of these theories to be important at the same time, and a black hole turns out to be one of the most ideal,” says theorist , also at UCSB.

Tensions rose in the 1970s, when physicists Jacob Bekenstein and Stephen Hawking showed that black holes must have a temperature. Bodies with a temperature have an associated entropy, and in quantum mechanics, entropy – a measure of a body’s disorder – implies the existence of a microstructure. Einstein’s equations, meanwhile, describe black holes as smooth, featureless distortions of space-time. Hawking also showed that quantum effects in and around the event horizon imply the black hole should steadily evaporate, emitting a stream of what we now call Hawking radiation.

But if a black hole does eventually dwindle to nothing, what happens to the stuff that falls in? At a fundamental level, matter and energy carry some information, and quantum mechanics says information cannot be destroyed. Perhaps the information encoded slips out with the Hawking radiation, but this idea runs into another problem: it leads to the black hole being surrounded by a “firewall” of blazing, energetic particles, again something general relativity forbids. In 2012, Polchinski, Marolf and their colleagues showed that black holes cannot simultaneously preserve information and possess an uneventful horizon (see diagram).

Disappearing act

This “firewall paradox” is still a hot topic. One emerging and tantalising suggestion is that the smooth fabric of Einsteinian space-time results from particles inside and outside the event horizon being linked quantum mechanically, via structures known as wormholes.

In August, speaking at a meeting in Stockholm, Sweden, Hawking set out an alternative stall, suggesting that information is never actually swallowed by a black hole. Instead, it persists at its event horizon in a form that is garbled and hard to decode. Last month, Nobel laureate Gerard ’t Hooft of Utrecht University in the Netherlands suggested that when matter and energy fall in, their information just bounces back.

Some sidestep such problems by returning to arguments reminiscent of Eddington’s and Einstein’s denial of black holes. Last year Laura Mersini-Houghton of the University of North Carolina, Chapel Hill, argued that massive stars cannot collapse to black holes – stops the star ever getting that far. So there are no event horizons and no singularities.

Few subscribe to that view, not least because of the considerable indirect observational evidence for black holes. Instead, the firewall paradox has opened up a new front in the struggle to unite general relativity and quantum mechanics. In that tussle, there’s a sense that the successful theory will be closer to quantum theory than general relativity, given the overwhelming success of quantum theory in explaining all the forces of nature besides gravity. Marolf, a general relativist, says he feels bad admitting that “general relativity is losing”. Einstein, who was troubled both by black holes and what he saw as quantum theory’s excesses, may have felt worse. Black holes could end up being the prediction that ate the theory.

Read more: “General relativity at 100: Einstein’s unfinished masterpiece”

This article appeared in print under the headline “General relativity at 100: The paradox of black holes”