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 theory of relativity, firstly, was not something that came out of nowhere. It required years of development, both mathematics-wise and physics-wise before Albert Einstein put it forward. Maybe, if I can say it so, it required all of the years before it, ever since the dawn of our race. In other words, it came at the time it had to come.
However, when it first showed up in scientific journals, it encountered great skepticism from the community. It was a shock to almost everyone not having the name of Albert Einstein. It needed a lot more years to be widely accepted and understood. The people who contributed to its understanding can be seen as visionaries, with more than an extraordinary intellect and great scientific intuition.
One of these people was Karl Schwarzschild, a now well-known scientist whose contributions span the fields of physics and astronomy but are based on the theory of relativity and his understanding of this.
Born in 1873, Schwarzschild showed great ability in the sciences from an early age, publishing papers on celestial orbits by 16. How incredible is that? Kids nowadays play on their phones at the age of 16, some not even knowing what their calling is. Well, little Karl sure did not have a phone, which most probably helped him find what interests him from an earlier age. Surprisingly, what we now call boredom can be pretty helpful since kids do a lot of interesting stuff when bored. They explore, try new things, and play, but with the things that surround them, with the real things, they are not trapped in virtual reality.
Anyways, after getting a relatively well-rounded education (which is very important), after having studied music, arts, Latin, and sciences, he finally obtained a doctorate at the Ludwig Maximilian University of Munich, under the supervision of Hugo von Seeliger, an astronomer.
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Establishment as an important figure, and working with the general theory of relativity
From then on, he got deeper into astronomy, working as an associate at the Kuffner Observatory in Austria. For a few years, he worked mostly with star clusters and photometry, developing a relationship between the luminosity of a star, the exposure time when observing, and the contrast created on the photographic plate.
He came to Gottingen in 1901 as a professor, and Gottingen was well-known for having some of the brightest scientists in physics at the time, such as David Hilbert or Hermann Minkowski (you might have heard about the latter as he was pivotal to the development of the special theory of relativity).
While serving on the front in Russia, around 1915, Schwarzschild started to think about the general theory of relativity. Despite also being ill, he managed to write three scientific papers, two of them regarding the general theory of relativity. He managed to provide the first exact solutions to Einstein’s field equations, something not even Einstein himself could do.
Albert Einstein had some approximate solutions to the equations, and he didn’t believe there could be any exact ones until Schwarzschild showed up. Einstein was delighted seeing Schwarzschild’s work, something he also wrote to him, in the words you’ve seen at the beginning of the article: 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 your mathematical treatment of the subject very much.
These solutions weren’t unique because they were exact; they’ve also been instrumental. Singularities have been a peculiarity in Einstein’s work, and nobody really understood what they should be. Truth is, we still don’t understand them, but it is clear that Einstein’s theory predicts them and allows their existence. From Schwarzschild’s solution, it can be seen that the singularity actually is somewhere specific, in a sphere of points, and the radius from the singularity to the edge of the sphere has the formula:
Where G is the gravitational constant, M is the body’s mass, and c is the velocity of light. This, of course, leads us to think about black holes, which is exactly where this formula can be used. If a body has a radius smaller than its Schwarzschild radius, it will inevitably collapse into a black hole. Funny, right? We are at no risk, though, since the Schwarzschild radius for a human is of the order of 10-23 cm. Also, you might know that black holes have an edge, which we call the event horizon, and the distance to that edge is exactly the Schwarzschild radius.
Schwarzschild died at the young age of 42 from a disease named pemphigus.