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We study the problem of stability and instability of extreme Reissner-Nordstrom spacetimes for linear scalar perturbations.
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D. Christodoulou, The Action Principle and Partial Differential Equations , Princeton University Press, New Jersey, 2000
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S. Alinhac, Geometric analysis of hyperbolic differential equations: An introduction
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H. Lindblad and I. Rodnianski, The global stability of Minkowski spacetime in harmonic gauge
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J. Marzuola, J. Metcalfe, D. Tataru, M. Tohaneanu, Strichartz estimates on Schwarzschild black hole backgrounds
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V. Schlue, Linear waves on higher dimensional Schwarzschild black holes
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