Event and Apparent Horizon Finders for 3 + 1 Numerical Relativity

Area of Science:

• Numerical relativity
• Black hole physics
• Computational astrophysics

Background:

• Event and apparent horizons are critical for identifying and characterizing black holes.
• Numerical relativity simulations generate spacetime data essential for horizon calculations.

Purpose of the Study:

• To review and compare numerical algorithms for finding event and apparent horizons.
• To focus on algorithms used within the 3+1 ADM formalism for spacetime computations.

Main Methods:

• Event horizon algorithms involve integrating null geodesics (forward/backward) or null surfaces (backward).
• Apparent horizon algorithms identify marginally outer trapped surfaces (MOTS) via nonlinear elliptic PDEs.
• Various algorithms exist for apparent horizons, including shooting, spectral, elliptic-PDE, pretracking, flow, and minimization methods, each with trade-offs.

Main Results:

• Backward null surface integration is generally the most efficient and accurate method for event horizons.
• Apparent horizon finders typically locate MOTSs, which approximate apparent horizons.
• Algorithm performance varies: shooting methods are good for axisymmetry; spectral and elliptic-PDE methods are fast but need good initial guesses; flow methods are robust but slow; minimization methods are faster in spectral codes.

Conclusions:

• The choice of algorithm for finding event and apparent horizons depends on the specific computational context and desired trade-offs.
• Accurate horizon calculations are vital for advancing our understanding of black hole physics through numerical simulations.