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Null Distance on a Spacetime

by Dr. Carlos Vega of Saint Louis U

  • Geometry/ Topology Seminar
  • Topology Seminar
When Tue, Sep 22, 2015
from 02:10 PM to 03:00 PM
Where 225 Ritter Hall
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Given any time function on a spacetime M, we define an induced null-distance function, built from and closely related to the causal structure of M. This null-distance is a conformal pseudometric in general, but is positive-definite under natural conditions. Further, in basic model cases, the causal structure is encoded completely in the resulting metric space.

In the cosmological setting, a canonical choice of time function was introduced and studied by Andersson, Galloway, and Howard. We show that under their basic `niceness' condition, the induced null distance is definite, and hence provides a uniform way of encoding `big bang' and related spacetimes as metric spaces. This is joint work with Christina Sormani.

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