On the occurrence of mass inflation for the Einstein-Maxwell-scalar field system with a cosmological constant and an exponential Price law

TL;DR

This paper investigates the stability and mass inflation phenomena inside black holes for the Einstein-Maxwell-scalar field system with a positive cosmological constant, revealing conditions under which strong cosmic censorship can be violated.

Contribution

It constructs characteristic initial data sets with exponential decay and analyzes their impact on mass inflation and the extendibility of spacetime across the Cauchy horizon.

Findings

Mass inflation may or may not occur depending on initial data decay rates.

Solutions can be extended across the Cauchy horizon with continuous metric and Christoffel symbols.

Violates the strong cosmic censorship conjecture under certain conditions.

Abstract

In this paper we study the spherically symmetric characteristic initial data problem for the Einstein-Maxwell-scalar field system with a positive cosmological constant in the interior of a black hole, assuming an exponential Price law along the event horizon. More precisely, we construct open sets of characteristic data which, on the outgoing initial null hypersurface (taken to be the event horizon), converges exponentially to a reference Reissner-N\"{o}rdstrom black hole at infinity. We prove the stability of the radius function at the Cauchy horizon, and show that, depending on the decay rate of the initial data, mass inflation may or may not occur. In the latter case, we find that the solution can be extended across the Cauchy horizon with continuous metric and Christoffel symbols in $L^2_{{\rm loc}}$, thus violating the Christodoulou-Chru\'sciel version of strong cosmic censorship.