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. Coley, A.A.; McNutt, D.D.: Horizon detection and higher dimensional black rings (2017)
  2. Clough, Katy; Figueras, Pau; Finkel, Hal; Kunesch, Markus; Lim, Eugene A.; Tunyasuvunakool, Saran: GRChombo: numerical relativity with adaptive mesh refinement (2015)
  3. Bentivegna, Eloisa; Korzyński, Mikołaj: Evolution of a periodic eight-black-hole lattice in numerical relativity (2012)
  4. Pfeiffer, Harald P.: Numerical simulations of compact object binaries (2012)
  5. Winicour, Jeffrey: Characteristic evolution and matching (2012)
  6. Ponce, Marcelo; Lousto, Carlos; Zlochower, Yosef: Seeking for toroidal event horizons from initially stationary BH configurations (2011)
  7. Zlochower, Yosef; Campanelli, Manuela; Lousto, Carlos O.: Modeling gravitational recoil from black-hole binaries using numerical relativity (2011)
  8. Centrella, Joan; Baker, John G.; Kelly, Bernard J.; van Meter, James R.: Black-hole binaries, gravitational waves, and numerical relativity (2010)
  9. Kelly, B.J.; Tichy, W.; Zlochower, Y.; Campanelli, M.; Whiting, B.: Post-Newtonian initial data with waves: progress in evolution (2010)
  10. Mars, Marc: Present status of the Penrose inequality (2009)
  11. Nielsen, Alex B.: Black holes and black hole thermodynamics without event horizons (2009)
  12. Jaramillo, José Luis; Valiente Kroon, Juan Antonio; Gourgoulhon, Eric: From geometry to numerics: Interdisciplinary aspects in mathematical and numerical relativity (2008)
  13. Herrmann, Frank; Hinder, Ian; Shoemaker, Deirdre; Laguna, Pablo: Unequal mass binary Black hole plunges and gravitational recoil (2007)
  14. Lin, Lap-Ming; Novak, Jér^ome: A new spectral apparent horizon finder for 3D numerical relativity (2007)
  15. Thornburg, Jonathan: Event and apparent horizon finders for $3+1$ numerical relativity (2007)
  16. Baiotti, Luca; Rezzolla, Luciano: Challenging the paradigm of singularity excision in gravitational collapse (2006)
  17. Pretorius, Frans: Simulation of binary black hole spacetimes with a harmonic evolution scheme (2006)
  18. Pretorius, Frans: Numerical relativity using a generalized harmonic decomposition (2005)
  19. Ashtekar, Abhay; Krishnan, Badri: Isolated and dynamical horizons and their applications (2004)
  20. Metzger, Jan: Numerical computation of constant mean curvature surfaces using finite elements (2004)

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