*In the last few doors of our advent calendar we explored black holes and Stephen Hawking's contribution to our understanding of them. Today we have a look at how all this fits together into the body of Hawking's life work.*

Ask a 12-year-old child to explain the Big Bang or a black hole and chances are you'll get a reasonably correct answer. Ask a physicist about the same concepts and he or she will tell you they are accepted components of our theory of the Universe. When Stephen Hawking started his career in the early 1960s neither of these two statements was true. The fact that they are now is to no small extent due to Hawking himself.

At the beginning of 1960s the idea that the Universe might have sprung from an extremely hot and dense beginning — a Big Bang – was hardly more than scientific speculation, much like the entire field of cosmology was barely considered a legitimate part of science. The then accepted theory of the history of the Universe, the *steady state theory*, held that the Universe had existed forever. Indeed, had Hawking been allowed to study under the PhD supervisor of his choice, the astronomer Fred Hoyle, he would have been drawn into defending this theory. As it happened, he helped to demolish it.

### From the Big Bang…

The discovery of the *cosmic microwave background* (CMB) radiation in 1964, which we will explore in upcoming doors of our advent calendar, provided the first nail in the coffin of the steady state theory. The theory couldn't explain the existence of this faint glow that permeated the Universe, but Big Bang theory could: the CMB might be nothing less than left over radiation from the Big Bang.

A map of the cosmic microwave background (CMB) formed from data taken by the Planck spacecraft. The varying colours represent tiny variations of the temperature of the CMB. These variations that give important clues about the nature of the Universe. Image: ESA and the Planck Collaboration.

Having begun his studies under Dennis Sciama instead of Hoyle, and influenced by the eminent Roger Penrose, Hawking began to investigate whether the general theory of relativity necessarily implied that the Universe started in an initial *singularity*. Another alternative to the steady state theory was that of a cyclical Universe, which eternally contracts to a hot and dense Big Bang-like state and then expands again. Working with George Ellis and Roger Penrose, Hawking eventually arrived at his famous singularity theorem: according to general relativity, an initial singularity was not only possible, it was inevitable. By the beginning of the 1970s Big Bang theory was fully accepted. Apart from its theoretical foundations, the Big Bang even owes its name to Hawking.

### ...to black holes

The Big Bang wasn't the only inevitable singularity, however. Hawking's work with Penrose showed that singularities would also occur inside *black holes*, regions of space within which the gravitational pull is so strong that nothing, not even light, can escape (or so it was thought). Black holes can arise, for example, when a massive star collapses under its own gravity.

Hawking's work on black holes, a natural step on from the Big Bang, established our current understanding of these gravitational monstrosities. Among other things, he discovered the notion of an *event horizon* of a black hole, the boundary of no return that surrounds the central singularity. He also proved his famous *area theorem*, which states that, no matter what happens to a black hole, the area of its event horizon can never become smaller. This hinted to a curious connection to a different part of physics, picked up by the young physicist Jacob Bekenstein: in thermodynamics there is a measure of the disorder of a physical system, called its *entropy*, which also never decreases. But since black holes were thought to be simple objects that didn't come with any degree of disorder — they were just black — this was thought a mere analogy without deeper meaning.

After a good run of work on black holes by Hawking and others, Hawking thought the field was all wrapped up. "I remember Stephen coming back [from a conference in 1973] and saying the subject is finished, we should look for another problem," says Gary Gibbons, Professor of Theoretical Physics at the Department of Applied Mathematics and Theoretical Physics and former student and collaborator of Hawking's. "So we started looking at a suggestion that he had made earlier: that there should be very small black holes formed in the early Universe. You should think of them as fossils of the Big Bang. If you could find them they would provide an important clue to the origin of the Universe."

A star is torn. This artist's impression shows a star approaching too close to a massive black hole and being torn apart by tidal forces. Image courtesy NASA's Goddard Space Flight Center/CI Lab.

Little did Hawking know at the time that these fossils' failure to exist would lead to his most celebrated result in black hole theory. While working with Gibbons, Hawking realised that even neutral, non-rotating primordial black holes would lose mass and would have evaporated long before our time. This amounted to a revolutionary statement. It said that black holes aren't completely black, but can emit thermal radiation — that's how they evaporate. The idea showed that black holes were in fact thermodynamic objects and turned Bekenstein's analogy to thermodynamics into a reality (you can find out more here). Hawking went on to formulate a thermodynamic theory of black holes, the central equation of which is the famous Bekenstein-Hawking entropy formula. "I would like this simple formula to be on my tombstone," Hawking said in his 60th birthday address.

Hawking's results on black holes were theoretical in nature. It wasn't until 2015 that the spectacular detection of gravitational waves opened up the possibility to test some of Hawking's results, including the area theorem, experimentally. "The data is not yet good enough to do this," Hawking said at his 75th birthday address last year. "But in the near future it should be possible [...]. With many more gravitational wave detections expected [...] I am excited by the possibilities the new era of gravitational wave astronomy will bring."

One theoretical problem about black holes, which has been causing physicists sleepless nights for decades, still remains open. If an object falls into a black hole, is the information that comes with it lost, or can it be recovered from the radiation when the black hole evaporates? If it were lost then a fundamental law of physics, the second law of thermodynamics, would be violated. This *information paradox* hugely intrigued Hawking. During the last years of his life Hawking, Malcolm Perry and Andrew Strominger worked hard on a mechanism that explains how information may be recovered.

Hawking's work has consequences for all of cosmology and even the whole of physics. Just as the singularity theorems applied to the "local" phenomenon of black holes and the "global" phenomenon of the Big Bang, his black hole radiation result may also illuminate the history of the Universe in its entirety. To find out more, read the full version of this article, which was publish on Hawking's death.

*This year's advent calendar was inspired by our work on the documentary series, Universe Unravelled, which explores the work done by researchers at the Stephen Hawking Centre for Theoretical Cosmology and is available on discovery+. Return to the 2020 Plus Advent Calendar.*