Event and Apparent Horizon Finders for 3+1 Numerical Relativity

Abstract

Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numerically-computed spacetimes, focusing on calculations done using the 3+1 ADM formalism. There are 3 basic algorithms for finding event horizons, based respectively on integrating null geodesics \emph{forwards} in time, integrating null geodesics \emph{backwards} in time, and integrating null \emph{surfaces} backwards in time. The last of these is generally the most efficient and accurate. There are a large number of apparent-horizon finding algorithms, with differing trade-offs between speed, robustness, accuracy, and ease of programming. In axisymmetry, shooting algorithms work well and are fairly easy to program. In slices with no continuous symmetries, Nakamura et al.'s algorithm and elliptic-PDE algorithms are fast and accurate, but require good initial guesses to converge. In many cases Schnetter's "pretracking" algorithm can greatly improve an elliptic-PDE algorithm's robustness. Flow algorithms are generally quite slow, but can be very robust in their convergence.

79 pages, 20 postscript figures including 12 in color, invited review article for Living Reviews in Relativity, uses epubtk.sty (included)

References in corpus (9)

• The Dynamics of General Relativity
• A single-domain spectral method for black hole puncture data
• Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole
• Non-symmetric trapped surfaces in the Schwarzschild and Vaidya spacetimes
• Black Holes Surrounded by Uniformly Rotating Rings
• Dynamical evolution of quasi-circular binary black hole data
• On the iterated Crank-Nicolson for hyperbolic and parabolic equations in numerical relativity
• Numerical computation of constant mean curvature surfaces using finite elements
• A fast apparent horizon algorithm

Cited by in corpus (5)

• Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme
• Initial Conditions for Numerical Relativity -- Introduction to numerical methods for solving elliptic PDEs
• Black holes as local horizons
• New frontiers in Numerical Relativity
• Curvature Invariants and the Geometric Horizon Conjecture in a Binary Black Hole Merger