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Costa, J. L., Girão, P. M., Natário, J. & Silva, J. S. (2015). On the global uniqueness for the Einstein–Maxwell-scalar field system with a cosmological constant: I. Well posedness and breakdown criterion. Classical and Quantum Gravity. 32 (1)

J. L. Costa et al.,  "On the global uniqueness for the Einstein–Maxwell-scalar field system with a cosmological constant: I. Well posedness and breakdown criterion", in Classical and Quantum Gravity, vol. 32, no. 1, 2015

@article{costa2015_1714610132952,
	author = "Costa, J. L. and Girão, P. M. and Natário, J. and Silva, J. S.",
	title = "On the global uniqueness for the Einstein–Maxwell-scalar field system with a cosmological constant: I. Well posedness and breakdown criterion",
	journal = "Classical and Quantum Gravity",
	year = "2015",
	volume = "32",
	number = "1",
	doi = "10.1088/0264-9381/32/1/015017",
	url = "http://iopscience.iop.org/0264-9381/32/1/015017/"
}

TY  - JOUR
TI  - On the global uniqueness for the Einstein–Maxwell-scalar field system with a cosmological constant: I. Well posedness and breakdown criterion
T2  - Classical and Quantum Gravity
VL  - 32
IS  - 1
AU  - Costa, J. L.
AU  - Girão, P. M.
AU  - Natário, J.
AU  - Silva, J. S.
PY  - 2015
SN  - 0264-9381
DO  - 10.1088/0264-9381/32/1/015017
UR  - http://iopscience.iop.org/0264-9381/32/1/015017/
AB  - This paper is the first 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 (MGHD) as a 'suitably regular' Lorentzian manifold. In this first part we establish well posedness of the Einstein equations for characteristic data satisfying the minimal regularity conditions leading to classical solutions. We also identify the appropriate notion of a maximal solution, from which the construction of the corresponding MGHD follows, and determine breakdown criteria. This is the unavoidable starting point of the analysis; our main results will depend on the detailed understanding of these fundamentals. In the second part of this series (Costa et al 2014, arXiv:1406.7253) we study the stability of the radius function at the Cauchy horizon. In the third and final paper (Costa et al 2014,arXiv:1406.7261) we show that, depending on the decay rate of the initial data, mass inflation may or may not occur; in fact, it is even possible to have (non-isometric) extensions of the spacetime across the Cauchy horizon as classical solutions of the Einstein equations.
ER  -