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

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.

7 pages, RevTex, to appear in CQG

References in corpus (2)

• QED commutation relations for inhomogeneous Kramers-Kronig dielectrics
• Boosted three-dimensional black-hole evolutions with singularity excision

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• Finite differencing second order systems describing black hole spacetimes
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