The interplay of mathematics and numerics in understanding naked singularity formation in critical collapse

Abstract: I will give an overview of numerical evidence that codimension one-sets of smooth initial data for matter coupled to GR form naked singularities - from scalar fields and fluids in spherical symmetry, where the evidence is strong, to vacuum GR, where the evidence is still confusing, but at least now beginning to be agreed by independent codes. Can one hope to prove some form of this naked singularity conjecture? In the last ten years or so, there has been considerable mathematical progress on the existence and stability of smooth self-similar blowup solutions in dispersive PDEs, and on naked singularity formation in GR. I will highlight some of these papers that particularly interest me as steps on the way to a future proof of naked singularity formation from codimension-one smooth initial data.

general relativity and quantum cosmologymathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

( video )

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JoMaReC - Joint Online Mathematical Relativity Colloquium

Series comments: This monthly online colloquium is meant to be accessible to and informative for mathematicians and mathematical physicists with a background in General Relativity, widely interpreted to include Lorentzian Geometry, and Geometric Analysis of various Partial Differential Equations related to General Relativity.

It is aimed to present motivation and applications of particular results and/or introduce specific subfields, while refraining from too much technicalities.

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