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Costa, J. L., Girão, P. M., Natário, J. & Drumond Silva, J. (2015). 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. Communications in Mathematical Physics. 339 (3), 903-947

J. L. Costa et al.,  "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", in Communications in Mathematical Physics, vol. 339, no. 3, pp. 903-947, 2015

@article{costa2015_1727914924970,
	author = "Costa, J. L. and Girão, P. M. and Natário, J. and Drumond Silva, J.",
	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",
	journal = "Communications in Mathematical Physics",
	year = "2015",
	volume = "339",
	number = "3",
	doi = "10.1007/s00220-015-2433-6",
	pages = "903-947",
	url = "http://link.springer.com/article/10.1007/s00220-015-2433-6?email.event.1.SEM.ArticleAuthorContributingOnlineFirst"
}

TY  - JOUR
TI  - 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
T2  - Communications in Mathematical Physics
VL  - 339
IS  - 3
AU  - Costa, J. L.
AU  - Girão, P. M.
AU  - Natário, J.
AU  - Drumond Silva, J.
PY  - 2015
SP  - 903-947
SN  - 0010-3616
DO  - 10.1007/s00220-015-2433-6
UR  - http://link.springer.com/article/10.1007/s00220-015-2433-6?email.event.1.SEM.ArticleAuthorContributingOnlineFirst
AB  - 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 ?, 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.
ER  -