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Foil 24 Linearization of Time Evolution Equations for q ij

From Numerical Formulation and Solution of Collision 0f two Black Holes CPSP713 Case studies in Computational Science -- Spring Semester 1996. by Geoffrey C. Fox


When Solving a second order time evolution equation such as
One typically converts this to a pair of first order in time equations by transformation:
We perform the analogous step in general relativity, introducing a new symmetric matrix K ij which is called the extrinsic curvature and related to but not exactly equal to single time derivative of q ij



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