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- TL;DR Summary
- Einstein, Infeld and Hoffman tried to derive the equations of motion of point particles in GR from Einstein's field equations
On another thread, now closed, Intrastellar asked:
Unfortunately it seems that thread is closed before anyone pointed out Einstein's papers on this question:
In 2019 Kiessling and Tahvildar-Zadeh argued that Einstein, Infeld and Hoffman made some mistakes in their treatment of charged particles, and they tried to fix those mistakes here:
Kiessling and Tahvildar-Zadeh say some interesting things about Einstein's original work on this:
Since the EFE describes the shape of spacetime, it describes the way black holes, for example, evolve. Can one derive the geodesic equation from it in some limit ?
Unfortunately it seems that thread is closed before anyone pointed out Einstein's papers on this question:
- A. Einstein, L. Infeld and B. Hoffman, The gravitational equations and the problem of motion, Annals of Mathematics 39 (1938), 65-100.
- A. Einstein and L. Infeld, The gravitational equations and the problem of motion, II, Annals of Mathematics 41 (1940), 455–464.
- A. Einstein and L. Infeld, On the motion of particles in general relativity theory, Canadian Journal of Physics 1 (1949), 209–241.
“I am plaguing myself with the derivation of the equations of motion of material points, conceived of as singularities [in the gravitational field], from the equations of general relativity.”
In 2019 Kiessling and Tahvildar-Zadeh argued that Einstein, Infeld and Hoffman made some mistakes in their treatment of charged particles, and they tried to fix those mistakes here:
- M. K.-H. Kiessling and A. S. Tahvildar-Zadeh, The Einstein-Infeld-Hoffmann legacy in mathematical relativity I: the classical motion of charged point particles.
Kiessling and Tahvildar-Zadeh say some interesting things about Einstein's original work on this:
We don’t know when Einstein first conceived of the notion of point particles as singularities in relativistic fields, but his letter to Max Born makes it plain that by the end of 1926 his ideas had matured to the point where he pursued a dynamical theory for such point singularities, expecting that their law of motion could be extracted from his gravitational field equations. Already a month later Einstein & Grommer announced that “the law of motion is completely determined by the field equations, though shown in this work only for the case of equilibrium.” In that paper the case of a static, spherically symmetric spacetime with a single time-like singularity was studied. The truly dynamical many-body problem was treated a decade later by Einstein, Infeld, and Hoffmann in their famous paper, with follow-ups in 1940 and 1949. They argued explicitly that the field equations of general relativity theory alone determine the equations of motion of neutral matter particles, viewed as point singularities in space-like slices of spacetime. They also claimed that they had generalized their results to charged point-singularities, with the details written up in a set of notes deposited with the secretary of the IAS. In 1941 the motion of charged point-singularities was revisited by Infeld’s student P. R.Wallace, who presented the details of the calculations in 1941. Here is the gist of the Einstein-Infeld-Hoffmann argument [...]
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