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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