Towards a Spacetime Intrinsic Flat Convergence

Abstract: In order to define a spacetime intrinsic flat convergence, Carlos Vega and I defined the null distance to convert spacetimes endowed with regular cosmological times into metric spaces. Currently Anna Sakovich and I have been exploring the properties of these metric spaces. We can prove that one can recover the causal structure from the null distance and the cosmological time. We can prove that a distance-preserving time-preserving bijection between the spacetimes endowed with a null distance is in fact a Lorentzian isometry under suitable conditions.  Next we will prove there are biLipschitz charts so that we may view the spacetimes endowed with the null distance as integral current spaces. This allows us to rigorously define the spacetime intrinsic flat convergence for spacetimes that arise as the future maximal developments of initial data sets. For more information about intrinsic flat convergence see sites.google.com/site/intrinsicflatconvergence/

general relativity and quantum cosmologymathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

( paper | 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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