A 3D Apparent Horizon Finder

TL;DR

This paper introduces a novel, efficient minimization-based method for locating apparent horizons in 3D black hole simulations, avoiding PDE boundary condition issues and enabling high parallelization.

Contribution

It presents a new minimization approach for finding apparent horizons that simplifies boundary condition handling and is suitable for parallel computing.

Findings

Effective in 2D and 3D cases

Highly parallelizable implementation

Avoids PDE boundary condition difficulties

Abstract

We report on an efficient method for locating the apparent horizon in numerically constructed dynamical 3D black hole spacetimes. Instead of solving the zero expansion partial differential equation, our method uses a minimization procedure. Converting the PDE problem to minimization eliminates the difficulty of imposing suitable boundary conditions for the PDE. We demonstrate the effectiveness of this method in both 2D and 3D cases. The method is also highly parallelizable for implementation in massively parallel computers.