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Complete Connection on the Causal Boundary of Spherically Symmetric Static Spacetimes

by Dr. Stacey Harris of Saint Louis U

  • Geometry/ Topology Seminar
  • Topology Seminar
When Tue, Oct 27, 2015
from 02:10 PM to 03:00 PM
Where 225 Ritter Hall
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Theoretical cosmology likes to make use of a "conformal boundary" for various spacetime models; this means mapping (via diffeomorphism on the image) a "physical" spacetime M into a "non-physical" spacetime M', such that the mapping is conformal (preserved causality) and the image of M has compact closure in M'--hence, M gets endowed with a boundary, inheriting geometry from M'.  One of the desireable properties of such a boundary is that it be complete in an appropriate sense.  A recent observation is that this is always possible for a static, spherically symmetric spacetime (or, at any rate, for physically reasonable ones).
But a conformal boundary is inherently a very ad hoc construction.  Is there any way to do this "naturally"?  The answer is yes:  The causal boundary construction is entirely natural (in a categorical sense), and it is well understood for static, spherically symmetric spacetimes.  The problem is that the causal boundary comes with a topology, but not a geometry--and it is geometry that is needed to answer the question about completeness.
This talk illustrates a method of imputing a linear connection on the causal boundary of a static, spherically symmetric spacetime.  There is not a unique way to do so, but all ways in this method agree on completeness.
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