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Nontrivial Spacetimes and the (Cosmological) Casimir Effect

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

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  1. 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 psutter2@uiuc.edu

  2. 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 psutter2@uiuc.edu

  3. 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 psutter2@uiuc.edu

  4. A Smorgasbord of (Flat) Spaces (Roboucas and Gomero, 2004) MWRM 16, Wash. U. in St. Louis 18 November 2006 psutter2@uiuc.edu

  5. A Smorgasbord of (Flat) Spaces (Roboucas and Gomero, 2004) Which one is our universe?? MWRM 16, Wash. U. in St. Louis 18 November 2006 psutter2@uiuc.edu

  6. 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 psutter2@uiuc.edu

  7. Flips and Position-Dependence y x MWRM 16, Wash. U. in St. Louis 18 November 2006 psutter2@uiuc.edu

  8. Patterns Third-Turn Space Hexagonal Cross-Section Quarter-Turn Space Rectangular Cross-Section MWRM 16, Wash. U. in St. Louis 18 November 2006 psutter2@uiuc.edu

  9. Hantzsche-Wendt Space z = 0.5 z = 1.0 z = 0.0 MWRM 16, Wash. U. in St. Louis 18 November 2006 psutter2@uiuc.edu

  10. The Dominance of the FP Quarter-Turn Half-Turn Third-Turn Sixth-Turn MWRM 16, Wash. U. in St. Louis 18 November 2006 psutter2@uiuc.edu

  11. The FP and Energy Density MWRM 16, Wash. U. in St. Louis 18 November 2006 psutter2@uiuc.edu

  12. You are here? MWRM 16, Wash. U. in St. Louis 18 November 2006 psutter2@uiuc.edu

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