A fast apparent horizon finder for three-dimensional Cartesian grids in numerical relativity. In 3 + 1 numerical simulations of dynamic black-hole spacetimes, it is 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 are 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 ∼10 -5 m accuracy on a GHz-class processor. I assume that an AH to be searched for is a Strahlkörper (`star-shaped region’) with respect to some local origin, and so parametrize the AH shape by r=h(angle) for some single-valued function h:S 2 →ℜ + . 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 six angular patches (one each in the neighbourhood of the ±x, ±y, and ±z axes) to avoid coordinate singularities, and finite difference the AH equation in the angular coordinates using fourth-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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  1. Cook, William G.; Wang, Diandian; Sperhake, Ulrich: Orbiting black-hole binaries and apparent horizons in higher dimensions (2018)
  2. Krawczynski, Henric: Difficulties of quantitative tests of the Kerr-hypothesis with X-ray observations of mass accreting black holes (2018)
  3. Coley, A. A.; McNutt, D. D.: Horizon detection and higher dimensional black rings (2017)
  4. Clough, Katy; Figueras, Pau; Finkel, Hal; Kunesch, Markus; Lim, Eugene A.; Tunyasuvunakool, Saran: GRChombo: numerical relativity with adaptive mesh refinement (2015)
  5. Brill, D.: History of a black hole horizon (2014)
  6. Bentivegna, Eloisa; Korzyński, Mikołaj: Evolution of a periodic eight-black-hole lattice in numerical relativity (2012)
  7. Pfeiffer, Harald P.: Numerical simulations of compact object binaries (2012)
  8. Winicour, Jeffrey: Characteristic evolution and matching (2012)
  9. Ponce, Marcelo; Lousto, Carlos; Zlochower, Yosef: Seeking for toroidal event horizons from initially stationary BH configurations (2011)
  10. Zlochower, Yosef; Campanelli, Manuela; Lousto, Carlos O.: Modeling gravitational recoil from black-hole binaries using numerical relativity (2011)
  11. Centrella, Joan; Baker, John G.; Kelly, Bernard J.; van Meter, James R.: Black-hole binaries, gravitational waves, and numerical relativity (2010)
  12. Kelly, B. J.; Tichy, W.; Zlochower, Y.; Campanelli, M.; Whiting, B.: Post-Newtonian initial data with waves: progress in evolution (2010)
  13. Mars, Marc: Present status of the Penrose inequality (2009)
  14. Nielsen, Alex B.: Black holes and black hole thermodynamics without event horizons (2009)
  15. Winicour, Jeffrey: Characteristic evolution and matching (2009)
  16. Jaramillo, José Luis; Valiente Kroon, Juan Antonio; Gourgoulhon, Eric: From geometry to numerics: Interdisciplinary aspects in mathematical and numerical relativity (2008)
  17. Herrmann, Frank; Hinder, Ian; Shoemaker, Deirdre; Laguna, Pablo: Unequal mass binary Black hole plunges and gravitational recoil (2007)
  18. Lin, Lap-Ming; Novak, Jérôme: A new spectral apparent horizon finder for 3D numerical relativity (2007)
  19. Thornburg, Jonathan: Event and apparent horizon finders for (3+1) numerical relativity (2007)
  20. Baiotti, Luca; Rezzolla, Luciano: Challenging the paradigm of singularity excision in gravitational collapse (2006)

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