The scientific paper occupying the mind of British physicist and cosmologist Stephen Hawking when he died in March aged 76 has been finished by colleagues from Cambridge and Harvard and published online.

Malcolm Perry, a professor of theoretical physics at Cambridge and a co-author of Black Hole Entropy and Soft Hair told the Guardian newspaper its subject, known as "the information paradox", was "at the center of Hawking's life" for 40 years.

"The difficulty is that if you throw something into a black hole, it looks like it disappears," the paper quoted Perry as saying. "How could the information in that object ever be recovered if the black hole then disappears itself?"

The quandary began with Albert Einstein who, in 1915, published his theory of general relativity, describing how gravity arises from the spacetime-bending effects of matter and explaining why planets circle the sun. Einstein also said black holes can be described by only three things: their mass, their charge, and their spin.

In Hawking's final paper, he and his collaborators add to Einstein's theories about black holes by trying to understand what happens to information when objects fall into black holes, the so-called information paradox.The analysis was completed days before Hawking's death and Perry said Hawking was delighted with the conclusion.

"It was very difficult for Stephen to communicate and I was put on a loudspeaker to explain where we had got to," Perry said. "When I explained it, he simply produced an enormous smile. I told him we'd got somewhere. He knew the final result."

In the paper, the team says black holes should be described by four attributes, not three, because they also have a temperature, and it is the fact that hot objects lose heat into space that means black holes are destined to evaporate out of existence.However, the rules of the quantum world say information can never be lost and Hawking and his colleagues contend that at least some information may be recorded by photons known as "soft hair" that surround the black hole's event horizon, which is the point at which light cannot escape the intense gravitational pull.

Physicists who worked on the paper included Sasha Haco from Cambridge and Andrew Strominger from Harvard.

Perry said the paper is an important step in understanding black holes but that "a lot more work" needs to be done.