Solving Einstein's Equations for Binary Black Hole Spacetimes

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General Relativity Theory II The spacetime metric ψ ab is determined by Einstein’s equation: R ab − 1 2 Rψ ab = 8πT ab , where R ab is the Ricci curvature tensor associated with ψ ab , R = ψ ab R ab is the scalar curvature, and T ab is the stress-energy tensor of the matter present in spacetime. For “vacuum” spacetimes (like binary black hole systems) T ab = 0, so Einstein’s equations can be reduced to R ab = 0. The Ricci curvature R ab is determined by derivatives of the metric: R ab = ∂ c Γ c ab − ∂ a Γ c bc + Γ c cdΓ d ab − Γ c adΓ d bc, where Γ c ab = 1 2 ψcd (∂ a ψ db + ∂ b ψ da − ∂ d ψ ab ). Lee Lindblom (Caltech) Binary Black Holes UW Milwaukee 10/14/2011 5 / 32
General Relativity Theory III Einstein’s equations are second-order PDEs that (should, hopefully) determine the spacetime metric, e.g. in vacuum R ab (∂∂ψ, ∂ψ, ψ) = 0. Lee Lindblom (Caltech) Binary Black Holes UW Milwaukee 10/14/2011 6 / 32
Page 1 and 2: Solving Einstein’s Equations for
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Page 9 and 10: General Relativity Theory Einstein
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Page 19 and 20: Gauge and Hyperbolicity in Electrom
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Page 29 and 30: The Constraint Problem Fixing the g
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Page 37 and 38: Outline of Talk: Brief History of t
Page 39 and 40: Numerical Solution of Evolution Equ
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Horizon Tracking Coordinates Coordi
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Horizon Distortion Maps Tidal defor
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Horizon Distortion Maps II Adjust t
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Caltech/Cornell Spectral Einstein C
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Accurate Long Waveform Simulations
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Post-Merger Recoils with Spin Merge
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High Spin Evolutions Lovelace, Sche
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Summary The NR community has made g
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Solving Einstein's Equations for Binary Black Hole Spacetimes

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