**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

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

**Einstein ring** Gravitational lensing

**If M* > 30 MS ** BLACK HOLE !

**Imaging Black Holes**

**curved spacetime** Newtonian spacetime

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

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

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

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

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

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

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

**See movie 1 ** Black hole in front of Magellanic Clouds

**Curved spacetime** Flat (Minskowski) spacetime Imaging spacetime : light cones

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

**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:

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

**Result for black hole** Outer solution only (Flamm paraboloid)

**v** u Spherical black hole in Kruskal coordinates

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

**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

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

**Cosmology**

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

**Expansion** Space-time curvature ==> a dynamical universe !

**Big bang models** open closed

**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

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

**A finite flat space without a boundary** • Torus

**horizon** Topological lens effect

**Physical Space** Observed Space Hypertorus

** Cosmic Microwave Background** The universe as a cosmic « drumhead »

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

**The CMB multipoles** Quadrupole

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

**• 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

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

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

**The « football Universe »** 36°

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

**J. Weeks, 2006**

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

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

**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

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