On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 3: Mass inflation and extendibility of the solutions

Abstract

This paper is the third 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 $\Lambda$, with the data on the outgoing initial null hypersurface given by a subextremal Reissner-Nordstrom black hole event horizon, study the future extendibility of the corresponding maximal globally hyperbolic development as a "suitably regular" Lorentzian manifold. In the first part of this series we established the well posedness of the characteristic problem, whereas in the second part we studied the stability of the radius function at the Cauchy horizon. In this third and final paper we show that, depending on the decay rate of the initial data, mass inflation may or may not occur. When the mass is controlled, it is possible to obtain continuous extensions of the metric across the Cauchy horizon with square integrable Christoffel symbols. Under slightly stronger conditions, we can bound the gradient of the scalar field. This allows the construction of (non-isometric) extensions of the maximal development which are classical solutions of the Einstein equations. Our results provide evidence against the validity of the strong cosmic censorship conjecture when $\Lambda >0$.

48 pages, 5 figures; v2: some presentation changes, mostly in the Introduction; v3: substantial changes in Section 5; v4: expanded Introduction; some presentation changes; matches final published version

References in corpus (4)

• The wave equation on Schwarzschild-de Sitter spacetimes
• Asymptotics of linear waves and resonances with applications to black holes
• 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
• On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 1: Well posedness and breakdown criterion

Cited by in corpus (30)

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• Strong Cosmic Censorship in higher-dimensional Reissner-Nordström-de Sitter spacetime
• Fate of Strong Cosmic Censorship Conjecture in Presence of Higher Spacetime Dimensions
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