Maria BabiucHamilton Department of Physics Marshall University Huntington WV April 7 2011 The Elusiveness Of Gravity What is Gravity Not an attraction force Matter distorts the spacetime geometry ID: 1044134
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1. BLACK HOLES SIMULATION and visualization Maria Babiuc-HamiltonDepartment of PhysicsMarshall University, Huntington, WV – April 7, 2011
2. The Elusiveness Of GravityWhat is Gravity? Not an attraction force!Matter distorts the space-time geometryThis distorted geometry makes matter move
3. Matter Is GeometryEinstein summarizes his Theory of General Relativity“People before me believed that if all the matter in the universe were removed, only space and time would exist. My theory proves that space and time would disappear along with matter”Empty space-time is flatCurvature of space-time (geometry)Arrangement of matter and energy
4. What Are Black HolesFirst and foremost implication of Einstein’s Theory of General RelativitySpace-time is so distorted by mass, that nothing, not even light can escape!The radius of no return forms the event horizon.The center is a “tear” in the fabric of space-time
5. Where Are Black HolesFormed from the supernova explosion of massive stars.“Supermassive” black holes at the center of all galaxies.Black holes can be:stationary or spinning , isolated or in an orbiting pair.
6. Gravitational WavesVibration in space-time due to accelerated mass, like:Supernovae explosions,Black holes spinning or in pairsWhy study it?New insights into:the formation of galaxiesbehavior, structure and history of space-timetest and validate alternative theories of gravity
7. A New AstronomyNormal Astronomy sees with “light waves” (visible, radio, x-rays…)Gravitational Wave Astronomy “sees” with gravitational wavesWhat will we “see”?colliding black holes,supernova explosions,the birth of the universethe structure of space-timeLaser Interferometer Gravitational-wave Observatory (LIGO)Laser Interferometer Space Array-not yet launched-
8. Catching the Wave in WVa
9. Detecting Gravity Waves in WVa
10. What Is DetectedLIGO and LISA will detect any small vibration, not only gravitational waves!Need models to know what to look for and tell the signal from the noise.Templates are essential for detection
11. Numerical RelativityUses computer codes to simulate black hole collisions and predict the gravitational wave signal for gravitational wave observatoriesKey tool to: Predict gravitational waveformsSimulate known astrophysical phenomenaDiscover new phenomena in general relativity
12. Black Hole Merger Simulation
13. Simulation ToolsCactus Code: Programming environment for High Performance ComputingEnables parallel computation on supercomputersAllows modular code development and large scientific collaborationsEinstein Toolkit: Modular computer codes for AstrophysicsSolves Einstein Equations and simulates space-timeBuilt-in codes that allow flexible input and output
14. Visualization ToolsThe simulation is run and a lot of numbers are produced: the DATA.A picture is worth a thousand “numbers.”We use the following free visualization tools to look at the data:GRACE: 2D plotting tool for X windows, running in all systems. http://plasma-gate.weizmann.ac.il/Grace/GNUPLOT: command line interactive plotting function, 1/2/3 D http://gnuplot.en.softonic.com/VISIT: visualization tool for parallel, interactive visualization of data https://wci.llnl.gov/codes/visit/
15. Einstein Equations Gmn = 8pTmnBlack holes are simple pure vacuum!Gmn = Rmn – 1/2gmnR = 0There is no known stable algorithmEinstein TensorMetric TensorCurvatureTensorCurvatureScalarGeometry(space-timeCurvature)Matter (mass and energy)
16. Inherent Difficulty How to simulate the singularity in a stable wayCoordinates need to be constructed during evolutionConservation laws impose constraints and overdetermine the evolutions
17. Ingredients of SimulationDecompose the space-time in space+time (foliate)Evolution:Solve constraints initiallyEvolve data Reconstruct the space-timeExtract the physics.Give Einstein Equations on the Initial Slice =foliate=Obtain Einstein Equations on the next sliceEvolve (step-up)In time
18. Initial DataSchwarzchildBrill-LindquistBoyer-YorkWormholeGeneral relativity depends on initial conditionsInitial data is specified on a slice of space-time that sufficiently determine the future evolution.
19. Harmonic EvolutionThe coordinates xm satisfy a wave equation xm=0 The vacuum Einstein equations reduce to 10 wave equations acting on the metric components gmnD’Alembertian
20. Numerical Approximationsfrom Calculus to Algebradu/dx = u(x+h)-u(x-x)/2h +O(h2)The accuracy of the simulation is given by the convergence of the code to the analytical solution.Problem: how to model infinite continuum space-time partial derivative with finite discrete numerical representation?
21. Well PosednessGiven a system of partially differential equations, well posedness means that: A solution existsThe solution is uniquePlus, the solution should be stable = depend continuously on the initial data.
22. Well PosednessProblems even with a “well posed” formulation: Grid induces high frequency modes Constraint violation exponential modes Solutions:Dissipation to control the high frequency modesConstraint adjustments to control exponential modes
23. Marching To InfinityHow to approach infinity when given only a finite amount of computer power and time?Go on a SUPECOMPUTER!One has to stop somewhere!Truncate the computational domain by introducing an artificial outer boundary sufficiently far from both the region where data is extracted.
24. When Is It Far Enough?The artificially introduced outer boundary is too far enough if:is causally disconnected from the dynamical parts of the simulationaccurately extrapolate the gravitational waveform at infinityaccounts for errors and perturbations without interfering with the simulated physics
25. The Boundary ProblemMust solve again the “well-posedness” problem.The outer boundary must be well posed:a unique solution, continuously dependent on the initial data, must existMoreover, the boundary must Control incoming radiationBe compatible with the constraintsBoundary dataneeds to be Well-posedArtificialboundarydue to limitedresources
26. Exploring Solutions Developed techniques to suppress exponentially growing instabilitiesImplemented stable and convergent outer boundary conditions of absorbing typeIntroduced a new formulation of constraint preserving boundary conditions for the general case of “moving boundaries”Implemented and testes with a 3D finite-difference general harmonic codeBuilding a pilot computational code with the purpose of introducing electromagnetic field and matter
27. Show Me The Physics!We proved the simulation is reliableThe data extracted will give information on the:motion of the Black Holeproperties of the Black Hole HorizonProblem: The emitted gravitational wave radiation has to be extracted at infinity, or adequately far from coalescing binary black hole!
28. A Rotating Black HoleThe metric over the whole run The lapse for the whole run
29. Two Inspiral Black HolesThe lapse for the whole runThe curvature
30. The Characteristic ApproachChoose a slicing condition to include a “null infinity” in the computational domain. Null infinity = the set of points which are approached asymptotically by light raysThe radial coordinate is “compactified”:r->x = r/(r+R)The waveform is evolved along the light ray and computed at null infinity
31. Binary-Black Hole WaveformsWaveform extraction form the inspiral and merger of two non-spinning black holes of equal massThe gravitational wave at the peak of the signalThe principal mode of the wave in time