Late-time tails and mass inflation for the spherically symmetric Einstein-Maxwell-scalar field system

Understand

We establish a decay result in the black hole exterior region of spherically symmetric solutions to the Einstein-Maxwell-scalar field system arising from compactly supported admissible data.

• Our result allows for large initial data, and it is the first decay statement for higher order derivatives of the scalar field.
• Solutions to this model generically develop a singularity in the black hole interior.
• Indeed, Luk--Oh (arxiv:1702.05715, arxiv:1702.05716) identify a generic class of initial data that produces $C^2$-future-inextendible solutions.