Celebratio Mathematica — Choquet-Bruhat

The Cauchy problem and beyond

Works connected to Julien Loizelet

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Y. Choquet-Bruhat, P. T. Chruściel, and J. Loizelet: “Global solutions of the Einstein–Maxwell equations in higher dimensions,” Classical Quantum Gravity 23 : 24 (2006), pp. 7383–7394. MR 2279722 Zbl 1117.83024 article

We consider the Einstein–Maxwell equations in space-dimension \( n \). We point out that the Lindblad–Rodnianski stability proof applies to those equations whatever the space-dimension \( n \geq 3 \). In even spacetime dimension \( n + 1 \geq 6 \), we use the standard conformal method on a Minkowski background to give a simple proof that the maximal globally hyperbolic development of initial data sets which are sufficiently close to the data for Minkowski spacetime and which are Schwarzschildian outside of a compact set lead to geodesically complete spacetimes, with a complete Scri, with a smooth conformal structure, and with the gravitational field approaching the Minkowski metric along null directions at least as fast as \( r^{-(n-1)/2} \).

Piotr T. Chruściel	Related
Julien Loizelet	Related