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Causal differencing of flux-conservative equations applied to black hole spacetimes

C. Gundlach·P. Walke
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Abstract

We give a general scheme for finite-differencing partial differential equations in flux-conservative form to second order, with a stencil that can be arbitrarily tilted with respect to the numerical grid, parameterized by a "tilt" vector field gamma^A. This can be used to center the numerical stencil on the physical light cone, by setting gamma^A = beta^A, where beta^A is the usual shift vector in the 3+1 split of spacetime, but other choices of the tilt may also be useful. We apply this "causal differencing" algorithm to the Bona-Masso equations, a hyperbolic and flux-conservative form of the Einstein equations, and demonstrate long term stable causally correct evolutions of single black hole systems in spherical symmetry.

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C. Gundlach, P. Walke. 1999-01-14. Causal differencing of flux-conservative equations applied to black hole spacetimes. https://doi.org/10.1088/0264-9381%2F16%2F3%2F026

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