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Costa, J. L. & Franzen, A. T. (2017). Bounded energy waves on the black hole interior of Reissner–Nordström–de Sitter. Annales Henri Poincaré. 18 (10), 3371-3398
J. L. Costa and A. T. Franzen, "Bounded energy waves on the black hole interior of Reissner–Nordström–de Sitter", in Annales Henri Poincaré, vol. 18, no. 10, pp. 3371-3398, 2017
@article{costa2017_1714986238645, author = "Costa, J. L. and Franzen, A. T.", title = "Bounded energy waves on the black hole interior of Reissner–Nordström–de Sitter", journal = "Annales Henri Poincaré", year = "2017", volume = "18", number = "10", doi = "10.1007/s00023-017-0592-z", pages = "3371-3398", url = "https://link.springer.com/article/10.1007/s00023-017-0592-z?wt_mc=Internal.Event.1.SEM.ArticleAuthorOnlineFirst" }
TY - JOUR TI - Bounded energy waves on the black hole interior of Reissner–Nordström–de Sitter T2 - Annales Henri Poincaré VL - 18 IS - 10 AU - Costa, J. L. AU - Franzen, A. T. PY - 2017 SP - 3371-3398 SN - 1424-0637 DO - 10.1007/s00023-017-0592-z UR - https://link.springer.com/article/10.1007/s00023-017-0592-z?wt_mc=Internal.Event.1.SEM.ArticleAuthorOnlineFirst AB - Motivated by the strong cosmic censorship conjecture, in the presence of a cosmological constant, we consider solutions of the scalar wave equation \Box _g\phi =0 on fixed subextremal Reissner–Nordström–de Sitter backgrounds ({\mathcal M}, g), without imposing symmetry assumptions on \phi . We provide a sufficient condition, in terms of surface gravities and a parameter for an exponential decaying Price Law, for a local energy of the waves to remain bounded up to the Cauchy horizon. The energy we consider controls, in particular, regular transverse derivatives at the Cauchy horizon; this allows us to extend the solutions with bounded energy, to the Cauchy horizon, as functions in C^0\cap H^1_\mathrm{loc}. Our results correspond to another manifestation of the potential breakdown of strong cosmic censorship in the positive cosmological constant setting. ER -