Stephen Hawking: Black holes, relativity and my eureka moment

From a lecture given at the University of Cambridge by the Lucasian Professor of Mathematics to mark his 60th birthday

I will skip over the first 20 of my 60 years, and pick up the story in October 1962, when I arrived in Cambridge as a graduate student. I had applied to work with Fred Hoyle, the principal defender of the steady state theory, and the most famous British astronomer of the time. However, Hoyle had enough students already, so to my great disappointment, I was assigned to Dennis Sharma, of whom I had not heard. But it was probably for the best, Hoyle was away a lot, seldom in the department, and I wouldn't have had much of his attention.

I followed the words and equations, but I didn't really get a feel for the subject. Also, I had been diagnosed with motor neurone disease, or ALS, and given to expect I didn't have long enough to finish my PhD. Then suddenly, towards the end of my second year of research, things picked up. My disease wasn't progressing much, and my work all fell into place, and I began to get somewhere.

The big question in cosmology in the early 60s was, did the universe have a beginning? Many scientists were instinctively opposed to the idea, because they felt that a point of creation would be a place where science broke down. One would have to appeal to the hand of God to determine how the universe would start off.

One scenario put forward was the steady-state theory in which, as the universe expanded, new matter was created to keep the density constant on average. This never had a very strong theoretical basis, but it had the great merit as a scientific theory of making definite predictions that could be tested by observations.

The final nail in the coffin of the steady-state theory came in 1965 with the discovery of a faint background of microwave radiation. The microwave background indicated that the universe had had a hot dense stage, in the past. But it didn't prove that was the beginning of the universe. One might imagine that the universe had had a previous contracting phase, and had bounced from contraction to expansion, at a high, but finite density. This was a fundamental question, and just what I needed to complete my PhD thesis.

Two Russians, Lifshitz and Khalatnikov, had claimed to have proved that a general contraction without exact symmetry, would always lead to a bounce, with the density remaining finite. This result was very convenient for Marxist-Leninist dialectical materialism, because it avoided awkward questions about the creation of the universe. It therefore became an article of faith for Soviet scientists.

Lifshitz and Khalatnikov were members of the old school in general relativity. That is, they wrote down a massive system of equations, and tried to guess a solution. But it wasn't clear that the solution they found, was the most general one. However, Roger Penrose introduced a new approach, which didn't require solving the field equations explicitly, just certain general properties, such as that energy is positive, and gravity is attractive. Penrose showed they were wrong. Small departures from spherical symmetry will not prevent a singularity.

I realised that similar arguments could be applied to the expansion of the universe. In this case, I could prove there were singularities where space-time had a beginning. General relativity predicted that the universe should have a beginning, a result that did not pass unnoticed by the Church.

My work on black holes began with a eureka moment in 1970, a few days after the birth of my daughter, Lucy. While getting into bed, I realised that I could apply to black holes, the causal structure theory I had developed for singularity theorems.

Our picture of the universe has changed a great deal in the last 40 years, and I'm happy if I have made a small contribution. I want to share my excitement and enthusiasm. There's nothing like the eureka moment, of discovering something that no one knew before. I won't compare it to sex, but it lasts longer.