The geodesic hypothesis in general relativity - Oxbridge PDE Days

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• Dr Shiwu Yang, DPMMS
• Friday 21 March 2014, 10:30-11:30
• MR2.

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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.

http://www.maths.cam.ac.uk/postgrad/cca/oxbridgepde2014.html

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