Abstract
We consider smooth solutions of the wave equation, on a fixed black hole region of a subextremal Reissner–Nordström (asymptotically flat, de Sitter or anti-de Sitter) spacetime, whose restrictions to the event horizon have compact support. We provide criteria, in terms of surface gravities, for the waves to remain in \(C^l\), \(l\geqslant 1\), up to and including the Cauchy horizon. We also provide sufficient conditions for the blow up of solutions in \(C^1\) and \(H^1\).
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Acknowledgements
We thank J. Natário and J. D. Silva for useful comments on a preliminary version of this paper. We also thank Anne Franzen for sharing and allowing us to use Fig. 1. This work was partially supported by FCT/Portugal through UID/MAT/04459/2013 and Grant (GPSEinstein) PTDC/MAT-ANA/1275/2014.
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Costa, J.L., Girão, P.M. Higher order linear stability and instability of Reissner–Nordström’s Cauchy horizon. Anal.Math.Phys. 10, 40 (2020). https://doi.org/10.1007/s13324-020-00380-5
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DOI: https://doi.org/10.1007/s13324-020-00380-5