The professor drew a box around the words and added "do not erase" at the bottom. That marked the opening of a two semester course in General Relativity. He never commented directly, but its presence was anything but subtle .

The circumstances under which Karl Schwarzchild wrote three significant papers in 1915 were a mixture of ideal and and anything but. An artillery lieutenant in the German army on the Russian front, he had contracted a disease that would kill him a year later Before the war he was a physicist and astronomer. In the army he managed to find access to current papers and had become fascinated with Albert Einstein's brand new General Theory of Relativity. The formula for General Relativity had written looks simple, but each symbol represents some very complex mathematical objects. Einstein was unable to solve them exactly and his prediction of the precession of the perihelion of Mercury's orbit was only an approximation.

It seems strange that Einstein, with his beautiful geometric approach to General Relativity, tried to solve the problem in rectangular coordinates. In a few months Schwarzschild created a novel coordinate system and was able to solve a simple system exactly with what is now known as the Schwarzschild metric. Schwarzschild sent it to Einstein for comments with this preface.

*As you see, the war treated me kindly enough, in spite of the heavy gunfire, to allow me to get away from it all and take this walk in the land of your ideas.*

Einstein was delighted

*I have read your paper with the utmost interest. I had not expected that one could formulate the exact solution of the problem in such a simple way. I liked very much your mathematical treatment of the subject. Next Thursday I shall present the work to the Academy with a few words of explanation.*

The simple case was simple indeed - a non-rotating spherically symmetric mass. Still there were remarkable conclusions. At long distances it reduced to Newton's gravitation equation, but close to a large mass there was a point where nothing - not even light - could escape from its surface. Any number of crazy things would happen as you neared this event horizon. Inside everything would collapse to a point - a singularity. Furthermore any initial configuration of matter (dust for example) would gravitationally attract and, if there was enough of it, collapse into a black hole.

About two weeks into the course we had enough differential geometry under our belts to look at the Schwarzschild metric. I remember looking up at the words on the upper right hand corner of the board and wondering why our Universe hadn't collapsed into a black hole - like almost instantly after it was formed. Wasn't there an enormous mass in a tiny space? I worked out the Schwartzschild radius for a mass the size of the universe in my notebook margin. Why didn't this happen?

The next week it became apparent why. The metric was for a static universe. General Relativity had a lot to say about non-static universes although that wasn't accepted until the next decade. There are a number of other metrics that apply to more complex, eg. realistic, universes that do things like expand or contract. One of these had major contributions from a Catholic priest who basically laid out the mathematical underpinnings of the expanding universe Hubble discovered in 1929, but that's another story.

Now it was easy to rule out a static universe .. immediately after the Big Bang (which turns out not to be the beginning) the new universe would find itself within a black hole and would have collapsed into itself. Or so I thought

There's something interesting about General Relativity - you've probably heard the presence of energy and matter curves spacetime. It turns out there's more - it also impacts the evolution of spacetime itself. There are three possibilities that depend on the initial expansion rate.

Too small for the amount of matter and energy and the universe would expand for awhile - perhaps the tiniest fraction of a second - and then collapse on itself. It's tempting to call it a black hole, but it's worse. Spacetime itself would collapse with it. Not very promising for life.

If the expansion rate was too high, matter would separate so quickly stars wouldn't form.. in fact atoms wouldn't form either. It's a bad sign if you can't make it to chemistry. Not good if you want life down the road.

There's an intermediate case. There's an exceedingly fine line between collapse into nothingness or expansion into a nearly void. Here the expansion rate eventually drops to zero with stars, galaxies, planets an us developing along the way. You want this one.

What we now know is a bit more complex. It's the third case, the goldilocks universe, but dark energy which is causing an accelerating expansion. It has been slow enough to allow the formation of everything we have. What really astounds me is the balance. The fine tuning of the right amount of expansion for the amount of mass energy is precise.. If there had been an extra hydrogen nucleus it would have collapsed. One less and the infinite expansion would have prevented the formation of complexity. The words on the blackboard seem much deeper to me now than they did at the time.

And if your name becomes associated with something in the public imagination there are always the joke. Einstein and SchrÃ¶dinger both mentioned cats so...

## Comments

You can follow this conversation by subscribing to the comment feed for this post.