Karl Schwarzschild: Solving GR on the Eastern Front

In summary, Karl Schwarzschild developed the solution to the Einstein field equation in 1915. He found a unique solution that reproduced the physics of the situation given the assumptions of vacuum and spherical symmetry.
  • #1
BWV
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Read the bio / fiction chapter on Karl Schwarzschild in Benjamin Labatut’s great Book, and curious on a little color on how he developed the solution - I had thought finding an exact solution in GR was just math chops, but actually any Lorentzian metric is an exact solution, so the difficulty was in finding a solution that reproduced the physics, but what physics would Swchwarzchild had in 1915 on the Eastern front - just the precession of Mercury, which was in the copy Einsteins GR paper he has?

FWIW, he was not directly in the trenches, he foolishly volunteered at age 40 to serve as an artillery specialist where he could employ abilities. He also was wasting away with Pemphigus, a nasty genetic skin disease that Ashkenazi Jews are susceptible to
 

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  • #2
BWV said:
what physics would Swchwarzchild had in 1915 on the Eastern front
He had Einstein's field equation; Einstein had sent him a preprint of his paper giving the final correct version of the field equation. He then looked for a solution that satisfied the assumptions of vacuum (zero stress-energy) and spherical symmetry, and found the solution that now bears his name. We now know that this is the unique solution for those conditions (this result is known as Birkhoff's Theorem and was proved, IIRC, in the early 1920s).

BWV said:
just the precession of Mercury, which was in the copy Einsteins GR paper he has?
Schwarzschild wasn't interested in solving the weak field limit; EInstein had already done that and showed that the precession of Mercury came out. He was interested in the most general possible solution for the conditions given (vacuum and spherical symmetry). (He also found a solution for the case of spherical symmetry and a perfect fluid with constant density, i.e., describing a highly idealized spherical planet or star.)
 
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  • #3
BWV said:
any Lorentzian metric is an exact solution
In the sense that you can compute its Einstein tensor and call that, adjusted by an appropriate constant factor, the "stress-energy tensor" of your solution, yes. But, as you note, this makes no guarantee whatever that the resulting solution will describe anything physically reasonable.

The more usual approach is to make some reasonable assumptions about things like symmetries of the spacetime (as Schwarzschild assumed spherical symmetry) and some general form for the stress-energy tensor (as Schwarzschild assumed vacuum, and then for his other solution he assumed a perfect fluid with constant density). That allows you to simplify the form of the metric using the symmetries, compute its Einstein tensor to give a set of differential equations for the metric components, and then use your assumption about the stress-energy tensor to determine the solution.
 
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Karl’s son Martin was an accomplished Astrophysicist, who fortunately fled Germany in the 30s and worked for US intelligence during the war, before landing at Princeton where he worked on stellar evolution, dying in 1997. No doubt some here knew him
 
  • #5
PeterDonis said:
He had Einstein's field equation; Einstein had sent him a preprint of his paper giving the final correct version of the field equation. He then looked for a solution that satisfied the assumptions of vacuum (zero stress-energy) and spherical symmetry, and found the solution that now bears his name. We now know that this is the unique solution for those conditions (this result is known as Birkhoff's Theorem and was proved, IIRC, in the early 1920s).
Amazingly, he also gave a first solution for a "compact star" (non-vacuum solution, using the model of an incompressible fluid). Both papers appeared in the "Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (Berlin) 1916":

https://ui.adsabs.harvard.edu/abs/1916SPAW...189S/abstract
https://ui.adsabs.harvard.edu/abs/1916skpa.conf..424S/abstract
 

FAQ: Karl Schwarzschild: Solving GR on the Eastern Front

1. Who was Karl Schwarzschild?

Karl Schwarzschild was a German physicist and astronomer who is best known for his contributions to the field of general relativity. He also made significant contributions to astrophysics and stellar dynamics.

2. What is "GR" in the context of Karl Schwarzschild?

"GR" stands for general relativity, which is a theory of gravitation developed by Albert Einstein. It describes how gravity works in the universe and has been confirmed by numerous experiments and observations.

3. How did Karl Schwarzschild solve GR on the Eastern Front?

Karl Schwarzschild solved GR on the Eastern Front by applying Einstein's equations to the problem of a spherically symmetric mass in a vacuum. He found a solution that is now known as the Schwarzschild metric, which describes the geometry of space-time around a non-rotating, uncharged mass.

4. What is the significance of Karl Schwarzschild's work on GR?

Karl Schwarzschild's work on GR was significant because it provided the first exact solution to Einstein's field equations. It also paved the way for further developments in the field of general relativity and helped to confirm its validity as a theory of gravity.

5. How has Karl Schwarzschild's work influenced modern science?

Karl Schwarzschild's work continues to influence modern science, particularly in the fields of astrophysics and cosmology. His solutions to Einstein's equations have been used to study black holes, gravitational waves, and the structure of the universe. His contributions to general relativity are still widely studied and applied in current research and technology.

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