Global Stability for Charged Scalar Fields in Spacetimes close to Minkowski
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Date
2018-03-22
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Johns Hopkins University
Abstract
In this work I prove global stability for the zero solution of the massless Charge-Scalar Field system on a background spacetime which is close to 1+3-dimensional Minkowski space. In particular, my analysis takes place in a class of background metrics which satisfy certain energy and decay estimates consistent with the behavior of small-data solutions to Einstein's Vacuum Equations in harmonic coordinates. My results are analogous to results obtained for the same system in Minkowski space by Lindblad and Sterbenz.
The proof relies on a single-parameter modification of the standard null frame and Lorentz fields which depends on the mass associated with the metric. In particular, the Lorentz fields are the same as those used in previous work by Hans Lindblad and the modified null frame can be written in terms of the modified Lorentz fields in a manner analogous to the standard null frame. This dissertation is based on my paper, Global Stability for Charged Scalar Fields in an Asymptotically Flat Metric in Harmonic Gauge
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Partial Differential Equations, Mathematical Relativity