einstein

Cosmology and Black Holes, 1917
CHAPTER ELEVEN
EINSTEIN’S UNIVERSE
1916–1919
In his Berlin home study
Cosmology is the study of the universe as a whole, including its size and shape, its history and destiny, from one end to the other, from the
beginning to the end of time. That’s a big topic. And it’s not a simple one. It’s not even simple to define what those concepts mean, or even if they
have meaning. With the gravitational field equations in his general theory of relativity, Einstein laid the foundations for studying the nature of the
universe, thereby becoming the primary founder of modern cosmology.
Helping him in this endeavor, at least in the early stages, was a profound mathematician and even more distinguished astrophysicist, Karl
Schwarzschild, who directed the Potsdam Observatory. He read Einstein’s new formulation of general relativity and, at the beginning of 1916, set
about trying to apply it to objects in space.
One thing made Schwarzschild’s work very difficult. He had volunteered for the German military during the war, and when he read Einstein’s
papers he was stationed in Russia, projecting the trajectory of artillery shells. Nevertheless, he was also able to find time to calculate what the
gravitational field would be, according to Einstein’s theory, around an object in space. It was the wartime counterpart to Einstein’s ability to come up
with the special theory of relativity while examining patent applications for the synchronization of clocks.
In January 1916, Schwarzschild mailed his result to Einstein with the declaration that it permitted his theory “to shine with increased purity.”
Among other things, it reconfirmed, with greater rigor, the success of Einstein’s equations in explaining Mercury’s orbit. Einstein was thrilled. “I
would not have expected that the exact solution to the problem could be formulated so simply,” he replied. The following Thursday, he personally
delivered the paper at the Prussian Academy’s weekly meeting. 1
Schwarzschild’s first calculations focused on the curvature of space-time outside a spherical, nonspinning star. A few weeks later, he sent
Einstein another paper on what it would be like inside such a star.
In both cases, something unusual seemed possible, indeed inevitable. If all the mass of a star (or any object) was compressed into a tiny enough
space—defined by what became known as the Schwarzschild radius—then all of the calculations seemed to break down. At the center, spacetime
would infinitely curve in on itself. For our sun, that would happen if all of its mass were compressed into a radius of less than two miles. For the
earth, it would happen if all the mass were compressed into a radius of about one-third of an inch.
What would that mean? In such a situation, nothing within the Schwarzschild radius would be able to escape the gravitational pull, not even light or
any other form of radiation. Time would also be part of the warpage as well, dilated to zero. In other words, a traveler nearing the Schwarzschild
radius would appear, to someone on the outside, to freeze to a halt.
Einstein did not believe, then or later, that these results actually corresponded to anything real. In 1939, for example, he produced a paper that
provided, he said, “a clear understanding as to why these ‘Schwarzschild singularities’ do not exist in physical reality.” A few months later, however,
J. Robert Oppenheimer and his student Hart-land Snyder argued the opposite, predicting that stars could undergo a gravitational collapse. 2
As for Schwarzschild, he never had the chance to study the issue further. Weeks after writing his papers, he contracted a horrible auto-immune
disease while on the front, which ate away at his skin cells, and he died that May at age 42.
As scientists would discover after Einstein’s death, Schwarzschild’s odd theory was right. Stars could collapse and create such a phenomenon,
and in fact they often did. In the 1960s, physicists such as Stephen Hawking, Roger Penrose, John Wheeler, Freeman Dyson, and Kip Thorne
showed that this was indeed a feature of Einstein’s general theory of relativity, one that was very real. Wheeler dubbed them “black holes,” and they
have been a feature of cosmology, as well as Star Trek episodes, ever since. 3
Black holes have now been discovered all over the universe, including one at the center of our galaxy that is a few million times more massive
than our sun. “Black holes are not rare, and they are not an accidental embellishment of our universe,” says Dyson. “They are the only places in the
universe where Einstein’s theory of relativity shows its full power and glory. Here, and nowhere else, space and time lose their individuality and
merge together in a sharply curved four-dimensional structure precisely delineated by Einstein’s equations.” 4
Einstein believed that his general theory solved Newton’s bucket issue in a way that Mach would have liked: inertia (or centrifugal forces) would
not exist for something spinning in a completely empty universe.* Instead, inertia was caused only by rotation relative to all the other objects in the
universe. “According to my theory, inertia is simply an interaction between masses, not an effect in which ‘space’ of itself is involved, separate from