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Abstract |
I am going to give a rigorous derivation of Einstein's geodesic hypothesis in general relativity. We use small material bodies governed by a class of nonlinear Klein-Gordon equations to approximate the test particle. Given a vacuum spacetime, we consider the initial value problem for the Einstein-scalar field system. For such particles with sufficiently small amplitude and size, we prove that the Einstein-scalar field system can be solved up to any given time. Moreover, the energy of the particle is concentrated along a time-like geodesic and the gravitational field produced by the particle is negligibly small in C^1, that is, the spacetime metric is C^1 close to the given vacuum metric. |
