University of Cambridge > > Geometric Analysis and Partial Differential Equations seminar > The global stability of the Minkowski spacetime solution to the Einstein-nonlinear electromagnetic system in wave coordinates

The global stability of the Minkowski spacetime solution to the Einstein-nonlinear electromagnetic system in wave coordinates

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  • UserJared Speck (Princeton)
  • ClockMonday 04 April 2011, 16:00-17:00
  • HouseCMS, MR13.

If you have a question about this talk, please contact Prof. Mihalis Dafermos.

The Einstein-nonlinear electromagnetic system is a coupling of the Einstein field equations of general relativity to nonlinear electromagnetic field equations. In this talk, I will discuss the family of covariant electromagnetic models that satisfy the following criteria: i) they are derivable from a sufficiently regular Lagrangian, ii) they reduce to the familiar Maxwell model in the weak-field limit, and iii) their corresponding energy-momentum tensors satisfy the dominant energy condition. I will mention several specific electromagnetic models that are of interest to researchers working in the foundations of physics. I will then discuss my main result, which is a proof of the global nonlinear stability of the 1 + 3 dimensional Minkowski spacetime solution to the coupled system. This stability result is a consequence of a small-data global existence result for a reduced system of equations that is equivalent to the original system in a wave coordinate gauge. The analysis of the spacetime metric components is based on a framework recently developed by Lindblad and Rodnianski, which allows one to derive suitable estimates for tensorial systems of quasilinear wave equations with nonlinearities that satisfy the weak null condition. The analysis of the electromagnetic fields, which satisfy quasilinear first-order equations, is based on an extension of a geometric energy-method framework developed by Christodoulou, together with a collection of pointwise decay estimates for the Faraday tensor that I develop. Throughout the analysis, I work directly with the electromagnetic fields, thus avoiding the introduction of electromagnetic potentials.

This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.

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