A Simplified Mathematical Model for the Formation of Null Singularities Inside Black Holes I - Basic Formulation and a Conjecture

Abstract

Einstein's equations are known to lead to the formation of black holes and spacetime singularities. This appears to be a manifestation of the mathematical phenomenon of finite-time blowup: a formation of singularities from regular initial data. We present a simple hyperbolic system of two semi-linear equations inspired by the Einstein equations. We explore a class of solutions to this system which are analogous to static black-hole models. These solutions exhibit a black-hole structure with a finite-time blowup on a characteristic line mimicking the null inner horizon of spinning or charged black holes. We conjecture that this behavior - namely black-hole formation with blow-up on a characteristic line - is a generic feature of our semi-linear system. Our simple system may provide insight into the formation of null singularities inside spinning or charged black holes in the full system of Einstein equations.

39 pages, 3 figures, extended version

References in corpus (15)

• Evanescent Black Holes
• Black hole singularities: a numerical approach
• Structure of the black hole's Cauchy horizon singularity
• Cosmic Censorship: As Strong As Ever
• Oscillatory null singularity inside realistic spinning black holes
• Stability of the Cauchy horizon in Kerr--de Sitter spacetimes
• The late-time singularity inside non-spherical black holes
• Structure of the Spherical Black Hole Interior
• Null weak singularities in plane-symmetric spacetimes
• Cauchy horizon singularity without mass inflation
• Semi-classical geometry of charged black holes
• The singularity in supercritical collapse of a spherical scalar field
• Global geometry of two-dimensional charged black holes
• Evaporation of a two-dimensional charged black hole
• A Simplified Mathematical Model for the Formation of Null Singularities Inside Black Holes II

Cited by in corpus (9)

• Particle Accelerators inside Spinning Black Holes
• The physics of the relativistic counter-streaming instability that drives mass inflation inside black holes
• Dynamical Collapse of Charged Scalar Field in Phantom Gravity
• Acceleration of particles near the inner black hole horizon
• Collapse of Charged Scalar Field in Dilaton Gravity
• Dilatons and the Dynamical Collapse of Charged Scalar Field
• Approximate solution to the CGHS field equations for two-dimensional evaporating black holes
• Asymptotics and singularities in cosmological models with positive cosmological constant
• A Simplified Mathematical Model for the Formation of Null Singularities Inside Black Holes II