I N T R O D U C T I O N T O V O L U M E 1 5 x l v i i For now, in his paper with Grommer, Einstein examines these solutions in detail, and uses them to argue that, according to general relativity, it is impossible for a particle to be subject to an external gravitational field and yet remain at rest. The argument depends on effectively distinguishing between acceptable and unaccept- able singularities in the spacetime metric. Einstein and Grommer allowed for sin- gularities to correspond to (or serve as placeholders for) material particles, but they did not allow singularities in regions of spacetime free of matter. Weyl’s papers on axialsymmetric solutions show that a solution to the vacuum Einstein equations ca- pable of representing a static two-body system would need to allow for a line sin- gularity between the two bodies. Thus, contrary to what Einstein thought when he first wrote of this solution to Rainich, upon closer inspection the solution must have been unacceptable to him as a physical solution representing two bodies at rest and interacting gravitationally. Einstein and Grommer modified the solution Weyl had interpreted as representing a static two-body system so that they could interpret it as representing one body subject to an external gravitational field. But the same argument applies: the solution is unacceptable because, in addition to the (accept- able) singularity corresponding to a material particle, it involves an (unacceptable) singularity along the rotation axis in spacetime regions free of matter. Einstein and Grommer thus effectively concluded that there is no physical solu- tion corresponding to a particle at rest but subject to an external gravitational field. They used this result to argue that, in general, the motions of particles can be de- termined from the vacuum field equations. As they note themselves, this would make general relativity unlike any of the theories that had preceded it (if, as did Einstein and Grommer, one disregards the approach featuring the energy- momentum tensor): for the first time, it would not be necessary to postulate both field equations and equations of motion for particles subject to the field in question. They began their argument by reformulating the vacuum Einstein equations in terms of a surface integral over a three-dimensional hypersurface, and defining gravitational energy-momentum flow through the surface. They then picked a curve that was supposed to represent the path of a material particle, imposed the linear approximation that the metric deviates only slightly from Minkowski space- time, and noted one of the main points made by Rainich: that not all solutions to the linearized field equations will correspond to solutions of the nonlinear vacuum Einstein equations that the linearized field equations approximate. However, they then proposed a potential solution to this problem that is not found in Einstein’s correspondence with Rainich: if a certain “equilibrium