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Introducing various notions of distances between space-times

Recent progress on geometric analysis and Riemannian geometry October 21, 2024 - October 25, 2024

October 25, 2024 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Anna Sakovich (Uppsala University)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Introducing various notions of distances between space-times

Abstract

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I will introduce the class of causally-null-compactifiable spacetimes that can be canonically converted into compact timed-metric spaces using the cosmological time function of Andersson-Galloway-Howard and the null distance of Sormani-Vega. This class of space-times includes future developments of compact initial data sets and regions exhausting asymptotically flat space-times. I will discuss various intrinsic notions of distance between such space-times and show that some of them are definite in the sense that they are equal to zero if and only if there is a time-oriented Lorentzian isometry between the space-times. These definite distances allow us to define notions of convergence of space-times to limit space-times that are not necessarily smoothThis is joint work with Christina Sormani.

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Introducing various notions of distances between space-times

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