A Simplified Mathematical Model for the Formation of Null Singularities Inside Black Holes II

Details A Simplified Mathematical Model for the Formation of Null Singularities Inside Black Holes II A Simplified Mathematical Model for the Formation of Null Singularities Inside Black Holes II

2006-12-27

arxiv.org/abs/gr-qc/0612173v1

J.Math.Phys.48:092503,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages, 10 figures

Scientific paper

10.1063/1.2779949

We study a simple system of two hyperbolic semi-linear equations, inspired by the Einstein equations. The system, which was introduced in gr-qc/0612136, is a model for singularity formation inside black holes. We show for a particular case of the equations that the system demonstrates a finite time blowup. The singularity that is formed is a null singularity. Then we show that in this particular case the singularity has features that are analogous to known features of models of black-hole interiors - which describe the inner-horizon instability. Our simple system may provide insight into the formation of null singularities inside spinning or charged black holes.

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