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Publication Detailed Description
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 Title
Communications in Mathematical Physics
Year (definitive publication)
2015
Language
English
Country
United States of America
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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 ?, 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.
Acknowledgements
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Keywords
Fields of Science and Technology Classification
- Mathematics - Natural Sciences
Funding Records
Funding Reference | Funding Entity |
---|---|
PEst-OE/EEI/LA0009/2013 | Fundação para a Ciência e a Tecnologia |
UTA_CMU/MAT/0007/2009 | Fundação para a Ciência e a Tecnologia |
PTDC/MAT/114397/2009 | Fundação para a Ciência e a Tecnologia |