An axisymmetric generalized harmonic evolution code

TL;DR

This paper introduces the first axisymmetric generalized harmonic evolution code for Einstein equations, demonstrating its robustness and exploring gravitational collapse in Kaluza-Klein spacetime, revealing complex black hole formation phenomena.

Contribution

It presents a novel axisymmetric numerical code based on the generalized harmonic formulation, capable of handling regular axes and studying scalar field collapse in higher-dimensional spacetimes.

Findings

The code successfully models gravitational collapse with black hole formation.

Damped wave gauge proves effective and robust for the simulations.

Near the threshold, multiple outcomes including black holes with different topologies emerge.

Abstract

We describe the first axisymmetric numerical code based on the generalized harmonic formulation of the Einstein equations which is regular at the axis. We test the code by investigating gravitational collapse of distributions of complex scalar field in a Kaluza-Klein spacetime. One of the key issues of the harmonic formulation is the choice of the gauge source functions, and we conclude that a damped wave gauge is remarkably robust in this case. Our preliminary study indicates that evolution of regular initial data leads to formation both of black holes with spherical and cylindrical horizon topologies. Intriguingly, we find evidence that near threshold for black hole formation the number of outcomes proliferates. Specifically, the collapsing matter splits into individual pulses, two of which travel in the opposite directions along the compact dimension and one which is ejected radially from the axis. Depending on the initial conditions, a curvature singularity develops inside the pulses.