Solving Einstein's Equations for Binary Black Hole Spacetimes

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Comparing Different Numerical Methods Wave propagation with second-order finite difference method: 3.0 3.0 3.0 N=200 N=200 N=200 2.5 t=0.0 2.5 t=100.0 2.5 t=200.0 2.0 2.0 2.0 U(x,t) 1.5 U(x,t) 1.5 U(x,t) 1.5 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0 π/2 π 3π/2 2π x 3.0 3.0 0.0 0 π/2 π 3π/2 2π x Wave propagation with spectral method: 0.0 0 π/2 π 3π/2 2π x 3.0 N=10 N=10 N=10 2.5 t=0.0 2.5 t=100.0 2.5 t=200.0 2.0 2.0 2.0 U(x,t) 1.5 U(x,t) 1.5 U(x,t) 1.5 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0 π/2 π 3π/2 2π x 0.0 0 π/2 π 3π/2 2π x Figures from Hesthaven, Gottlieb, & Gottlieb (2007). 0.0 0 π/2 π 3π/2 2π x Lee Lindblom (Caltech) Binary Black Holes UW Milwaukee 10/14/2011 19 / 32
Moving Black Holes in a Spectral Code Spectral: Excision boundary is a smooth analytic surface. Lee Lindblom (Caltech) Binary Black Holes UW Milwaukee 10/14/2011 20 / 32
Page 1 and 2: Solving Einstein’s Equations for
Page 3 and 4: History of Numerical Solution of th
Page 5 and 6: History of Numerical Solution of th
Page 7 and 8: Outline of Talk: Brief History of t
Page 9 and 10: General Relativity Theory Einstein
Page 11 and 12: General Relativity Theory Einstein
Page 13 and 14: General Relativity Theory II The sp
Page 15 and 16: General Relativity Theory III Einst
Page 17 and 18: General Relativity Theory III Einst
Page 19 and 20: Gauge and Hyperbolicity in Electrom
Page 21 and 22: Gauge and Hyperbolicity in Electrom
Page 23 and 24: Gauge and Hyperbolicity in General
Page 25 and 26: Gauge and Hyperbolicity in General
Page 27 and 28: The Constraint Problem Fixing the g
Page 29 and 30: The Constraint Problem Fixing the g
Page 31 and 32: Constraint Damping in Electromagnet
Page 33 and 34: Generalized Harmonic Evolution Syst
Page 35 and 36: Constraint Damping Generalized Harm
Page 37 and 38: Outline of Talk: Brief History of t
Page 39 and 40: Numerical Solution of Evolution Equ
Page 41 and 42: Numerical Solution of Evolution Equ
Page 43 and 44: Basic Numerical Methods Different n
Page 45 and 46: Basic Numerical Methods Different n
Page 47 and 48: Basic Numerical Methods II A few gr
Page 49 and 50: Basic Numerical Methods II A few gr
Page 51: Comparing Different Numerical Metho
Page 55 and 56: Moving Black Holes in a Spectral Co
Page 65 and 66: Horizon Tracking Coordinates Coordi
Page 67 and 68: Horizon Distortion Maps Tidal defor
Page 69 and 70: Horizon Distortion Maps II Adjust t
Page 71 and 72: Caltech/Cornell Spectral Einstein C
Page 73 and 74: Accurate Long Waveform Simulations
Page 75 and 76: Post-Merger Recoils with Spin Merge
Page 77 and 78: High Spin Evolutions Lovelace, Sche
Page 79: Summary The NR community has made g

Solving Einstein's Equations for Binary Black Hole Spacetimes

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