Black-hole collisions and gravitational waves U. Sperhake CSIC-IEEC Barcelona California Institute of Technology University of Mississippi Física, Porto, 2 nd September 2010 U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 1 / 72
Overview Motivation Introduction Ingredients of numerical relativity Results Precambrium: before the 2005 explosion Gravitational wave observations Black holes in astrophysics Black holes in fundamental physics Summary U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 2 / 72
1. Motivation U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 3 / 72
Black holes in Astrophysics Black holes are important in many astrophysical processes Galaxies host BHs Important sources of electromagnetic radiation Structure formation in the Universe U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 4 / 72
Black holes in Astrophysics Black holes are important in many astrophysical processes Structure of galaxies Cosmic projectiles U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 5 / 72
Black holes in Fundamental Physics Black holes allow new tests of fundamental physics Strongest sources of Gravitational Waves (GWs) Test alternative theories of Gravity No-hair theorem of GR U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 6 / 72
Black holes in Fundamental Physics Black holes allow new tests of fundamental physics Production in particle accelerators U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 7 / 72
Black holes in Fundamental Physics LHC CERN U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 8 / 72
Black holes in Fundamental Physics BH evaporation via Hawking radiation U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 9 / 72
Black holes in Fundamental Physics BH spacetimes “know” about physics without BHs AdS-CFT Correspondence U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 10 / 72
2. What are Black Holes? U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 11 / 72
How to characterize Black HoleS? Consider Lightcones In and outgoing light Calculate surface of outgoing light fronts Expansion ≡ Rate of change of this surface Apparent Horizon ≡ Outermost surface with zero expansion “Light cones tip over” due to curvature U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 12 / 72
Schwarzschild metric Unfortunate coordinates Singularity at r = 2 M What does this mean? U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 13 / 72
Kruskal coordinates U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 14 / 72
Kruskal coordinates U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 15 / 72
Kruskal coordinates U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 16 / 72
Penrose diagram U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 17 / 72
Rotating BHs: Kerr metric U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 18 / 72
Rotating BHs: Kerr BH U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 19 / 72
Penrose diagram U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 20 / 72
BHs for astrophysicists Supermassive BHs found at center of virtually all galaxies U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 21 / 72
Stellar BHs In stellar binary systems: Cygnus XR-1 U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 22 / 72
Stellar BHs X ray source! U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 23 / 72
Stellar BHs One member is very compact and massive ⇒ Black Hole! U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 24 / 72
Stellar BHs Mass transfer, accretion U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 25 / 72
How are Black Holes formed? Stellar BHs: Supernovae U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 26 / 72
3. Gravitational Wave observations U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 27 / 72
Gravitational Waves Einstein’s equations have wave like solutions: Gravitational Waves: h ij = h ij ( r − t ) Effect on test particles U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 28 / 72
Gravitational Wave detectors Accelerated masses generate GWs Interaction with matter very weak! Earth bound detectors: GEO600, LIGO, TAMA, VIRGO U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 29 / 72
Detection principle Principle of measurement: Michelson-Morley interferometer but muuuuuuuch more accurate: fraction of nucleus per km U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 30 / 72
Space interferometer LISA U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 31 / 72
Pulsar timing arrays U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 32 / 72
Expected sources U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 33 / 72
Expected sources U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 34 / 72
Some targets of GW physics Confirmation of GR Hulse & Taylor 1993 Nobel Prize Parameter determination of BHs: M , � S Optical counter parts Standard sirens (candles) Mass of graviton Test Kerr Nature of BHs Cosmological sources Neutron stars: EOS U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 35 / 72
Some targets of GW physics U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 36 / 72
GW physics with LISA U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 37 / 72
GW physics with LISA U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 38 / 72
GW physics with LISA U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 39 / 72
Matched filtering U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 40 / 72
3. Numerical Framework U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 41 / 72
General Relativity: Curvature Curvature generates acceleration “geodesic deviation” No “force”!! Description of geometry Metric g αβ Γ α Connection βγ R αβγδ Riemann Tensor U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 42 / 72
The metric defines everything Christoffel connection 2 g αµ ( ∂ β g γµ + ∂ γ g µβ − ∂ µ g βγ ) Γ α βγ = 1 Covariant derivative ∇ α T βγ = ∂ α T βγ + Γ β µα T µγ − Γ µ γα T βµ Riemann Tensor µγ Γ µ µδ Γ µ R αβγδ = ∂ γ Γ α βδ − ∂ δ Γ α βγ + Γ α βδ − Γ α βγ ⇒ Geodesic deviation, Parallel transport, ... U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 43 / 72
How to get the metric? The metric must obey the Einstein Equations Ricci-Tensor, Einstein Tensor, Matter Tensor R αβ ≡ R µαµβ G αβ − 1 2 g αβ R µµ “Trace reversed” Ricci T αβ “Matter” Einstein Equations G αβ = 8 π T αβ Solutions: Easy! Take metric ⇒ Calculate G αβ ⇒ Use that as matter tensor Physically meaningful solutions: Difficult! U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 44 / 72
The Einstein Equations in vacuum “Spacetime tells matter how to move, matter tells spacetime how to curve” Field equations in vacuum: R αβ = 0 Second order PDEs for the metric components Invariant under coordinate (gauge) transformations System of equations extremely complex: Pile of paper! Analytic solutions: Minkowski, Schwarzschild, Kerr, Robertson-Walker, ... Numerical methods necessary for general scenarios!!! U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 45 / 72
A list of tasks Target: Predict time evolution of BBH in GR Einstein equations: 1) Cast as evolution system 2) Choose specific formulation 3) Discretize for computer Choose coordinate conditions: Gauge Fix technical aspects: 1) Mesh refinement / spectral domains 2) Singularity handling / excision 3) Parallelization Construct realistic initial data Start evolution and waaaaiiiiit... Extract physics from the data U. Sperhake (CSIC-IEEC) Black-hole collisions and gravitational waves 02/09/2010 46 / 72
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