# Stephen Hawking’s ‘final paper’ on hairy black holes hits the headlines

A few days after Stephen Hawking died in March, you might recall us covering what we said was the great cosmologist’s “last” paper. Now, however, it seems that the article wasn’t actually his last: the *Guardian* is running two stories about what it dubs Hawking’s “final” scientific paper. And in what seems a carefully planned publicity exercise, Hawking’s “final book” is scheduled for publication next week too.

Uploaded to the *arXiv *preprint server last week and updated on Tuesday, Hawking’s “final” paper is called “Black hole entropy and soft hair”. It contains calculations that aim to help solve the “information paradox” that arises when stuff is sucked into a black hole.

Conventional thinking going back to Albert Einstein is that a black hole can be described only in terms of its mass and spin. This is the “no-hair” theorem, the idea being that like bald heads, black holes have few features to distinguish themselves. No-hair means that information about the physical state of matter must be lost as the matter is sucked into a black hole – otherwise, this information would distinguish one black hole from another.

In 1974 Hawking made the landmark conjecture that black holes do not simply suck in everything, but rather behave as black bodies that emit radiation as well as absorbing it. He calculated the black-body temperature of a black hole using an equation that now graces his memorial in Westminster Abbey.

### Microscopic arrangements

Having a distinct temperature implies that a black hole has entropy, which Hawking also calculated. Entropy is a measure of the number of different ways the microscopic constituents of a black hole can arrange themselves. This goes against the no-hair theorem, which says that a black hole can only be arranged in one way – as defined by its mass and spin.

In 2015, Hawking teamed up with his Cambridge colleague Malcolm Perry and Harvard University’s Andrew Strominger to address the decades old paradox. A year later the trio published a paper that suggested that information-preserving massless particles known as “soft hair” could surround black holes.

In this latest research, Hawking, Perry and Strominger joined forces with Cambridge’s Sasha Haco to calculate the entropy of a black hole that has a certain kind of soft hair. The physicists conclude that their result agrees with Hawking’s original calculation of black-hole entropy.

Writing in one of the *Guardian* articles, Perry says “While this is not a resolution of the information paradox, we believe it provides some considerable insight into it”.

Is this Hawking’s last paper? Perry describes it as “perhaps the last paper that Stephen was involved in,” so maybe there are more out there.

And if you cannot get enough Hawking, the celebrated cosmologist’s last book will be published on 16 October. Stay tuned to *Physics World *for a review of the book and much more next week.