Finding Apparent Horizons in Dynamic 3D Numerical Spacetimes

Abstract

We have developed a general method for finding apparent horizons in 3D numerical relativity. Instead of solving for the partial differential equation describing the location of the apparent horizons, we expand the closed 2D surfaces in terms of symmetric trace--free tensors and solve for the expansion coefficients using a minimization procedure. Our method is applied to a number of different spacetimes, including numerically constructed spacetimes containing highly distorted axisymmetric black holes in spherical coordinates, and 3D rotating, and colliding black holes in Cartesian coordinates.

19 pages, 13 figures, LaTex, to appear in Phys. Rev. D. Minor changes made

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• Introduction to Isolated Horizons in Numerical Relativity
• Numerical Relativity and Compact Binaries
• Black Hole Boundary Conditions and Coordinate Conditions
• Pseudo-spectral apparent horizon finders: an efficient new algorithm
• Moving Black Holes in 3D
• Black hole excision with matching
• Numerical simulations of black-hole binaries and gravitational wave emission
• Three-dimensional simulations of distorted black holes. I. Comparison with axisymmetric results
• The existence and stability of marginally trapped surfaces
• A new spectral apparent horizon finder for 3D numerical relativity
• Finding apparent horizons and other two-surfaces of constant expansion
• Locating Boosted Kerr and Schwarzschild Apparent Horizons
• Generic Tracking of Multiple Apparent Horizons with Level Flow
• Horizon Pretracking
• Multipole moments on the common horizon in a binary-black-hole simulation
• A 3+1 Computational Scheme for Dynamic Spherically Symmetric Black Hole Spacetimes -- I: Initial Data
• Apparent Horizon Formation and Hoop Conjecture in Non-axisymmetric Spaces
• A 3+1 Computational Scheme for Dynamic Spherically Symmetric Black Hole Spacetimes -- II: Time Evolution