The Einstein-Infeld-Hoffmann Legacy in Mathematical Relativity
Einstein's General Relativity Theory is usually summarized, in a nutshell, as follows: ``Matter tells spacetime how to curve, and spacetime curvature tells matter how to move.'' In particular, one learns that uncharged point particles of rest mass m move along (time-like) geodesics. This law of geodetic motion is based on the notion of ``test particle'' --- a theoretical fiction which assumes that the contribution of the very point particle to the curvature of spacetime can be ignored. In their Annals of Mathematics paper of 1938, Albert Einstein, Leo Infeld, and Banesh Hoffmann tried to go beyond this test-particle fiction by arguing that Einstein's gravitational field equations would also dictate the motion of point particles which ``do tell spacetime how to curve.'' Needless to say that their paper was not mathematically rigorous by modern standards; worse, their claim cannot be true the generality in which the claims was made. In this course I first explain the physical background, then formulate the problem mathematically sharply, then survey what's rigorously known about it, and last not least I point the student to important open problems which have resisted the attempts of mathematical relativists so far.
501, 561, or special permission by the instructor
Professor Kiessling's lecture notes