Stephen Hawking's final scientific paper has been released, and it deals with one of the central topics in the physicist's 56-year-long career.
The work was completed in the days before Hawking's death in March.
It tackles the question of whether black holes preserve information on the stuff that falls into them.
Some researchers had believed this information was destroyed, but others said that this violated the laws of quantum mechanics.
These laws propose that everything in our world can be broken down into information, for example, a string of 1s and 0s. In addition, this information should never disappear, not even if it gets sucked into a black hole.
But Hawking, building on the work of Albert Einstein, showed that black holes have a temperature. And because hot objects lose heat into space, black holes must eventually evaporate - disappearing from existence.
Black holes themselves are regions in space where the gravity is so strong that nothing that gets pulled in can escape.
Writing in the Guardian, one of the study's co-authors, Malcolm Perry, from the University of Cambridge, said: "What Hawking discovered was that in black hole physics, there seemed to be even greater uncertainty than in quantum mechanics."
He added: "That might not have mattered - except that black holes are real physical objects. There are huge black holes at the centres of many galaxies."
If an object has a temperature, it will also have a property known as entropy.
"The entropy is a measure of how many different ways an object can be made from its microscopic ingredients and still look the same," said Prof Perry.
He says that he discussed the paper with Hawking shortly before he died, but wasn't aware the professor was ill.
"It was very difficult for Stephen to communicate and I was put on a loudspeaker to explain where we had got to. When I explained it, he simply produced an enormous smile," Prof Perry explained.
The new paper shows mathematically that the entropy of a black hole may be recorded by the particles of light (photons) that surround the black hole's event horizon. The event horizon is a boundary, or point of no return, where escape from the gravitational pull of the black hole becomes impossible - including for light.
The patina of light around the black hole has been dubbed "soft hair". "What this paper does is show that 'soft hair' can account for the entropy," said Prof Perry.
But he added that : "We don't know that Hawking entropy accounts for everything you could possibly throw at a black hole, so this is really a step along the way."
Hawking's most important discoveries
- With the Oxford mathematician Roger Penrose, he showed that if there was a Big Bang, it must have started from an infinitely small point - a singularity
- Black holes radiate energy known as Hawking radiation, while gradually losing mass. This is due to quantum effects near the edge of the black hole, a region called the event horizon
- He predicted the existence of mini-black holes at the time of the Big Bang. These tiny black holes would have been incredibly hot, shedding mass until they vanished - potentially ending their lives in a powerful explosion.
- In the 70s, Hawking considered whether the particles and light entering a black hole were destroyed if the black hole evaporated. Hawking initially thought this "information" was lost from the Universe. But US physicist Leonard Susskind disagreed. These ideas became known as the information paradox. In 2004, Hawking conceded that the information must be conserved.
- With the physicist James Hartle, he tried to describe the history of the cosmos in one mathematical expression. But quantum theory shows that the distinctions between space and time are unclear. As a result, the proposal showed there was little point asking what happened before the Big Bang.
Now Prof Perry and the remaining authors have to find out how the information associated with a black hole's entropy is physically stored in the soft hair, and how that information comes out of a black hole when it evaporates.
The research builds on previous work published in 2015, which suggested that information might not make it into a black hole, but is held on its boundary.
Prof Marika Taylor, a theoretical physicist at the University of Southampton, said: "The authors have to make several non-trivial assumptions so the next steps will be to show that these assumptions are valid."
Previously, Prof Hawking had proposed that photons could be emitted from black holes due to quantum fluctuations, a concept known as Hawking radiation. Information from the black hole might be able to escape via this route, but it might be in a chaotic, useless form.