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

TL;DR

This paper investigates the extendibility of solutions in the Einstein-Maxwell-scalar field system with a positive cosmological constant, showing conditions under which mass inflation occurs or is avoided, impacting the strong cosmic censorship conjecture.

Contribution

It demonstrates how decay rates of initial data influence mass inflation and solution extendibility, providing new insights into the structure of black hole interiors with a cosmological constant.

Findings

Mass inflation depends on initial data decay rates.

Continuous metric extensions are possible under controlled mass inflation.

Results challenge the strong cosmic censorship conjecture for positive b3.

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 $\Lambda>0$.