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Nontrivial Spacetimes and the (Cosmological) Casimir Effect. Paul Matthew Sutter University of Illinois at Urbana-Champaign. With: Tsunefumi Tanaka Humboldt State University, Arcata, CA. preprint available at: gr-qc/0610051. (M.C. Escher). The (Non-cosmological) Casimir Effect.

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Nontrivial spacetimes and the cosmological casimir effect l.jpg
Nontrivial Spacetimesand the (Cosmological) Casimir Effect

Paul Matthew Sutter

University of Illinois at Urbana-Champaign

With:

Tsunefumi Tanaka

Humboldt State University, Arcata, CA

preprint available at:

gr-qc/0610051

(M.C. Escher)

MWRM 16, Wash. U. in St. Louis

18 November 2006

[email protected]


The non cosmological casimir effect l.jpg
The (Non-cosmological) Casimir Effect

(Courtesy of CIPA)

Boundary conditions affect vacuum energy density between plates

MWRM 16, Wash. U. in St. Louis

18 November 2006

[email protected]


Constructing a universe l.jpg
Constructing a Universe

  • We are going to construct

  • “multiply-connected” topologies:

  • Take a basic geometric object

  • (a “Fundamental Polyhedron”, or FP)

  • and identify opposite sides.

  • “Multiply-connected”:

  • more than one path between x and x’

  • The “curvature” of a cylinder is extrinsic

  • (i.e. not a property of the space itself)

MWRM 16, Wash. U. in St. Louis

18 November 2006

[email protected]


A smorgasbord of flat spaces l.jpg
A Smorgasbord of (Flat) Spaces

(Roboucas and Gomero, 2004)

MWRM 16, Wash. U. in St. Louis

18 November 2006

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A smorgasbord of flat spaces5 l.jpg
A Smorgasbord of (Flat) Spaces

(Roboucas and Gomero, 2004)

Which one is our universe??

MWRM 16, Wash. U. in St. Louis

18 November 2006

[email protected]


Sutter s seven simple steps to success l.jpg

Choose field….......................

Choose geometry…..............

Choose topology…...............

Determine spacetime interval……………………...

Try to evaluate …..

Renormalize with Method of Images…............................

Publish!...................................

massless scalar

flat!

Klein space, 3-Torus, etc…

Sutter, P.M. and Tanaka, T. Phys. Rev. D 74, 024023 (2006)

Sutter’s Seven Simple Steps to Success

MWRM 16, Wash. U. in St. Louis

18 November 2006

[email protected]


Flips and position dependence l.jpg
Flips and Position-Dependence

y

x

MWRM 16, Wash. U. in St. Louis

18 November 2006

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Patterns l.jpg
Patterns

Third-Turn Space

Hexagonal Cross-Section

Quarter-Turn Space

Rectangular Cross-Section

MWRM 16, Wash. U. in St. Louis

18 November 2006

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Hantzsche wendt space l.jpg
Hantzsche-Wendt Space

z = 0.5

z = 1.0

z = 0.0

MWRM 16, Wash. U. in St. Louis

18 November 2006

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The dominance of the fp l.jpg
The Dominance of the FP

Quarter-Turn

Half-Turn

Third-Turn

Sixth-Turn

MWRM 16, Wash. U. in St. Louis

18 November 2006

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The fp and energy density l.jpg
The FP and Energy Density

MWRM 16, Wash. U. in St. Louis

18 November 2006

[email protected]


Slide12 l.jpg

You are here?

MWRM 16, Wash. U. in St. Louis

18 November 2006

[email protected]


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