Global solutions of the Einstein-Maxwell equations in higher dimensions

Abstract

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 $n\ge 3$. In even space-time dimension $n+1\ge 6$ 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 space-time and which are Schwarzschildian outside of a compact set lead to geodesically complete space-times, with a complete Scri, with smooth conformal structure, and with the gravitational field approaching the Minkowski metric along null directions at least as fast as $r^{-(n-1)/2}$.

minor corrections

References in corpus (6)

• Global existence for the Einstein vacuum equations in wave coordinates
• Existence of non-trivial, vacuum, asymptotically simple space-times
• Asymptotic Flatness and Bondi Energy in Higher Dimensional Gravity
• Asymptotically simple solutions of the vacuum Einstein equations in even dimensions
• Conformal Null Infinity Does Not Exist for Radiating Solutions in Odd Spacetime Dimensions
• Critical behavior in vacuum gravitational collapse in 4+1 dimensions

Cited by in corpus (17)

• Numerical Methods for Finding Stationary Gravitational Solutions
• BMS Supertranslations and Memory in Four and Higher Dimensions
• The Cauchy problem on a characteristic cone for the Einstein equations in arbitrary dimensions
• Topological censorship for Kaluza-Klein space-times
• Decay of linear waves on higher dimensional Schwarzschild black holes
• Stability of Minkowski space and polyhomogeneity of the metric
• Interpreting spacetimes of any dimension using geodesic deviation
• Peeling of the Weyl tensor and gravitational radiation in higher dimensions
• The Global Stability of the Minkowski Spacetime Solution to the Einstein-Nonlinear Electromagnetic System in Wave Coordinates
• Dynamical systems with benign ghosts
• Attractors of the Einstein-Klein Gordon system
• Asymptotic behaviour of Maxwell fields in higher dimensions
• Asymptotic behaviour of the Weyl tensor in higher dimensions
• The Weak Null Condition and Kaluza-Klein Spacetimes
• The asymptotics of stationary electro-vacuum metrics in odd space-time dimensions
• Snell's law for the Schwarzschild black hole
• Electrodynamics in flat spacetime of six dimensions