2020/01/31 by Maxime Van de Moortel, Maxime Van de Moortel · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cauchy distribution #Cauchy problem #Circular symmetry #Cosmic censorship hypothesis #Cosmology and Gravitation Theories #Event horizon #Horizon #Inflation (cosmology) #Initial value problem #Noncommutative and Quantum Gravity Theories #Scalar field #gr-qc #math-ph #math.AP #math.MP
paper · pdf · doi:10.1007/s00220-020-03923-w
Versions accepted for publication in Communications in Mathematical Physics
openalex created_date 2020/02/07 · arxiv created 2020/08/20 · openalex publication_date 2021/01/02 · arxiv updated 2021/02/03 · openalex updated_date 2026/08/05
It has long been suggested that the Cauchy horizon of dynamical black holes is subject to a weak null singularity, under the mass inflation scenario. We study in spherical symmetry the Einstein-Maxwell-Klein-Gordon equations and while we do not directly show mass inflation, we obtain a "mass inflation/ridigity" dichotomy. More precisely, we prove assuming (sufficiently slow) decay of the charged scalar field on the event horizon, that the Cauchy horizon emanating from time-like infinity is CHi+= D ∪ S for two (possibly empty) disjoint connected sets D and S such that: _D (the dynamical set) is a past set on which the Hawking mass blows up (mass inflation scenario). _S (the static set) is a future set isometric to a Reissner--Nordström Cauchy horizon i.e. the radiation is zero on S. As a consequence, we establish a novel classification of Cauchy horizons into three types: dynamical (S=∅), static (D=∅) or mixed, and prove that CHi+ is globally C2-inextendible. Our main motivation is the C2 Strong Cosmic Censorship Conjecture for a realistic model of spherical collapse in which charged matter emulates the repulsive role of angular momentum: in our case the Einstein-Maxwell-Klein-Gordon system on one-ended space-times. As a result, we prove in spherical symmetry that: - two-ended asymptotically flat space-times are C2-future-inextendible i.e. C2 Strong Cosmic Censorship is true for Einstein-Maxwell-Klein-Gordon, assuming the decay of the scalar field on the event horizon at the expected rate. - In the one-ended case, the Cauchy horizon emanating from time-like infinity is C2-inextendible. This result suppresses the main obstruction to C2 Strong Cosmic Censorship in spherical collapse.