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Title: On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 2: structure of the solutions and stability of the cauchy horizon
Authors: Costa, J. L.
Girão, P. M.
Natário, J
Drumond Silva, J.
Issue Date: 2015
Publisher: Springer Berlin Heidelberg
Abstract: This paper is the second part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein–Maxwell-scalar field system with a cosmological constant Λ, with the data on the outgoing initial null hypersurface given by a subextremal Reissner–Nordström black hole event horizon, study the future extendibility of the corresponding maximal globally hyperbolic development as a “suitably regular” Lorentzian manifold. In the first paper of this sequence (Costa et al., Class Quantum Gravity 32:015017, 2015), we established well posedness of the characteristic problem with general initial data. In this second paper, we generalize the results of Dafermos (Ann Math 158:875–928, 2003) on the stability of the radius function at the Cauchy horizon by including a cosmological constant. This requires a considerable deviation from the strategy followed in Dafermos (Ann Math 158:875–928, 2003), focusing on the level sets of the radius function instead of the red-shift and blue-shift regions. We also present new results on the global structure of the solution when the free data is not identically zero in a neighborhood of the origin. In the third and final paper (Costa et al., On the global uniqueness for the Einstein–Maxwell-scalar field system with a cosmological constant. Part 3. Mass inflation and extendibility of the solutions. arXiv:​1406.​7261, 2015), we will consider the issue of mass inflation and extendibility of solutions beyond the Cauchy horizon.
Description: WOS:000360090500004 (Nº de Acesso Web of Science)
Peer reviewed: Sim
ISSN: 0010-3616
Publisher version: The definitive version is available at:
Appears in Collections:BRU-RI - Artigo em revista científica internacional com arbitragem científica

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