Finding Apparent Horizons in Dynamic 3D Numerical Spacetimes

TL;DR

This paper introduces a new general method for locating apparent horizons in 3D numerical relativity by expanding surfaces in symmetric trace-free tensors and solving for coefficients through minimization, applicable to various complex spacetimes.

Contribution

The paper presents a novel approach for finding apparent horizons in 3D numerical spacetimes that avoids solving PDEs directly, using tensor expansions and minimization techniques.

Findings

Successfully applied to highly distorted axisymmetric black holes

Effective in 3D rotating and colliding black hole spacetimes

Demonstrates versatility across different coordinate systems

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.