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The Shape of Space: from Black Holes to the Universe

Imaging in Space and Time 28/8-1/9 2006 Brijuni. The Shape of Space: from Black Holes to the Universe. J.-P.Luminet Observatoire de Paris (LUTH). Cosmic topology. Cosmology. Black holes. ?. Quantum gravity. 4 levels of geometry. ds 2 = g ij dx i x j. spacetime metric.

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The Shape of Space: from Black Holes to the Universe

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  1. Imaging in Space and Time 28/8-1/9 2006 Brijuni The Shape of Space:from Black Holes to the Universe J.-P.Luminet Observatoire de Paris (LUTH)

  2. Cosmic topology Cosmology Black holes ? Quantum gravity 4 levels of geometry

  3. ds2 = gij dxixj spacetime metric General Relativity Gij = k Tij geometry = matter-energy gravity = spacetime curvature

  4. Einstein ring Gravitational lensing

  5. If M* > 30 MS BLACK HOLE !

  6. Imaging Black Holes

  7. curved spacetime Newtonian spacetime

  8. Image of a spherical black hole with thin accretion disk (J.-P. Luminet, 1979)

  9. Flight into a black hole (J.A.Marck, 1993)

  10. Black hole in front of Milky Way (Riazuelo, 2006)

  11. Capella Castor & Pollux Aldebaran Orion Sirius Black hole in front of Constellations

  12. Capella 1 Aldebaran 2 Orion 2 Capella 2 Einstein ring Orion 1 Aldebaran 1 Imaging spacetime : light cones

  13. Southern Cross Canopus a & b Cen Achernar Black hole in front of Magellanic Clouds

  14. Southern Cross 1 Canopus 1 Achernar 2 a & b Cen 2 Southern Cross 2 Canopus 2 Einstein ring Achernar 1

  15. See movie 1 Black hole in front of Magellanic Clouds

  16. Curved spacetime Flat (Minskowski) spacetime Imaging spacetime : light cones

  17. metric: Schwarzschild radius: Event horizon Gravitational collapse to a Schwarzschild black hole

  18. Equatorial section Time section Curved 2-geometry: Embedding in 3D Euclidian space Embedding Step 1: Schwarzschild metric outside mass M (G=c=1) : Step 2: Step 3:

  19. Result for ordinary star (R* > 2M) Outer solution (asymptotically flat) Inner solution (regular)

  20. Result for black hole Outer solution only (Flamm paraboloid)

  21. v u Spherical black hole in Kruskal coordinates

  22. Flight into a static black hole Radial photons (A.Riazuelo, 2006) What is seen in C What is seen in E See movie 1

  23. Flight into a static black hole 2 Non-radial photons What is seen in E What is seen further What is seen in C See movie 2

  24. Flight into a Kerr (rotating) black hole no movie yet!

  25. Cosmology

  26. finite (no edge) Homogeneity => constant space curvature ! espace sphérique finite or infinite espace Euclidien finite or infinite espace hyperbolique

  27. Expansion Space-time curvature ==> a dynamical universe !

  28. Big bang models open closed

  29. G G G G G G G G Horizon Horizon Horizon G G G T T T Infini Assumption 1 Assumption 2 Assumption 3 Universe is finite (without boundary) but greater than the observable one Universe is finite (without boundary) and smaller than the observable one Universe is infinite What is the size and shape of space ? Not testable (only L >> Rh) May be testable • if L >~ Rh Testable • topological lensing

  30. Hypersphere = 3D space finite volume, no edge Lignes droites Think finite space without edge Sphere = 2D Surfacefinite area, no edge

  31. A finite flat space without a boundary • Torus

  32. horizon Topological lens effect

  33. Physical Space Observed Space Hypertorus

  34. Cosmic Microwave Background The universe as a cosmic « drumhead »

  35. Spherical harmonics us Multipole moments Cosmic Microwave Background Observed on a 2-sphere

  36. The CMB multipoles Quadrupole

  37. Power spectrum dTl2 = l(l+1)Cl/2p Doppler peaks (Boomerang, Archeops, etc.) l=180°/q Large scales (COBE, WMAP)

  38. • Universe seems to be positively curved W = 1.02 ± 0.02 • Lack of power at large scales (> 60°) Space might be finite with a special shape! WMAP power spectrum(2003- 2006) flat infinite universe

  39. Poincaré Dodecahedral SpaceFP : 12 faces regular dodecahedron 120 copies tessellate S3 S3/I*

  40. Poincaré Dodecahedral Spherical space (PDS) • fit low quadrupole • fit low octopole •  < Wtot < 1.02 Planck Surveyor (2007) Luminet et al., Nature 425, 593 (2003)

  41. The « football Universe » 36°

  42. Tetrahedral space (Wtot > 1.025) Also compatible … Octahedral space (Wtot > 1.015)

  43. J. Weeks, 2006

  44. Quantum foam (J. Wheeler) Imaging Quantum Gravity

  45. Solution 1 : string theory Price to pay : extra-dimensions Veneziano, Green, Schwarz, Witten, etc. Closed string Open string bulk

  46. Atoms of space: 10-99 cm3 Atoms of time : 10-43 sec Spin network Spin foam Knot theory Solution 2 : loop quantum gravity Ashtekhar, Smolin, Rovelli, Bojowald

  47. If God had consulted me before embarking upon Creation, I should have recommended something simpler.Alfonso X, King of Castile

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