2024/12/23 by Onyx Gautam, Gautam, Onyx · 3 citations
Earth and Planetary Sciences · Physics and Astronomy · #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Gravity Measurements #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2412.17927
openalex publication_date 2024/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 C2-future-inextendible solutions. However, they leave open the question of mass inflation: does the Hawking mass become identically infinite at the Cauchy horizon? By work of Luk--Oh--Shlapentokh-Rothman (arxiv:2201.12294), our decay result implies mass inflation for sufficiently regular solutions in the generic class considered by Luk--Oh (arxiv:1702.05715, arxiv:1702.05716). Together with the methods and results of Luk--Oh (arXiv:2404.02220), our estimates imply a late-time tails result for the scalar field. This result provides another proof of generic mass inflation, through a result of Dafermos (arXiv:arch-ive/0307013). Another application of our late-time tails result, due to Van de Moortel, is the global construction of two-ended black holes that contain null and spacelike singularities.