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A Fast Apparent-Horizon Finder for 3-Dimensional Cartesian Grids in Numerical Relativity

8 Pith papers cite this work. Polarity classification is still indexing.

8 Pith papers citing it
abstract

In 3+1 numerical simulations of dynamic black hole spacetimes, it's useful to be able to find the apparent horizon(s) (AH) in each slice of a time evolution. A number of AH finders are available, but they often take many minutes to run, so they're too slow to be practically usable at each time step. Here I present a new AH finder,_AHFinderDirect_, which is very fast and accurate: at typical resolutions it takes only a few seconds to find an AH to $\sim 10^{-5} m$ accuracy on a GHz-class processor. I assume that an AH to be searched for is a Strahlk\"orper (star-shaped region) with respect to some local origin, and so parameterize the AH shape by $r = h(angle)$ for some single-valued function $h: S^2 \to \Re^+$. The AH equation then becomes a nonlinear elliptic PDE in $h$ on $S^2$, whose coefficients are algebraic functions of $g_{ij}$, $K_{ij}$, and the Cartesian-coordinate spatial derivatives of $g_{ij}$. I discretize $S^2$ using 6 angular patches (one each in the neighborhood of the $\pm x$, $\pm y$, and $\pm z$ axes) to avoid coordinate singularities, and finite difference the AH equation in the angular coordinates using 4th order finite differencing. I solve the resulting system of nonlinear algebraic equations (for $h$ at the angular grid points) by Newton's method, using a "symbolic differentiation" technique to compute the Jacobian matrix._AHFinderDirect_ is implemented as a thorn in the_Cactus_ computational toolkit, and is freely available by anonymous CVS checkout.

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gr-qc 8

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2026 5 2025 3

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representative citing papers

Lessons from binary dynamics of inspiralling equal-mass boson-star mergers

gr-qc · 2026-04-28 · unverdicted · novelty 7.0

Numerical simulations of equal-mass boson-star mergers reveal larger waveform deviations from black-hole binaries in late inspiral and merger, plus odd multipole excitations for certain scalar-field phases, with some signals degenerate until IMR consistency tests are applied.

Ringdown and lensing of triple systems

gr-qc · 2026-05-19 · conditional · novelty 6.0

Head-on black-hole mergers next to a companion show Doppler- and redshift-shifted ringdown, lensing magnification behind the lens, and delayed echo images, with only tentative signs of resonant mode excitation.

Cusp Formation in Merging Black Hole Horizons

gr-qc · 2026-05-11 · unverdicted · novelty 6.0 · 2 refs

Numerical study of cusp formation on horizons in head-on non-spinning black hole mergers, with analysis of mass and multipole behavior at the cusp and a proposed phenomenological model.

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